Thu Sep 13 13:01:17 2018 PROB_TEST Python version: 3.6.5 Test the PROB library. ANGLE_CDF_TEST Python version: 3.6.5 ANGLE_CDF evaluates the Angle CDF PDF parameter N = 5 PDF argument X = 0.5 CDF value = 0.0107809 ANGLE_CDF_TEST Normal end of execution. ANGLE_MEAN_TEST Python version: 3.6.5 ANGLE_MEAN computes the Angle mean PDF parameter N = 5 PDF mean = 1.5708 ANGLE_MEAN_TEST Normal end of execution. ANGLE_PDF_TEST Python version: 3.6.5 ANGLE_PDF evaluates the Angle PDF PDF parameter N = 5 PDF argument X = 0.5 PDF value = 0.0826466 ANGLE_PDF_TEST Normal end of execution. ANGLIT_CDF_TEST Python version: 3.6.5 ANGLIT_CDF evaluates the Anglit CDF ANGLIT_CDF_INV inverts the Anglit CDF. ANGLIT_PDF evaluates the Anglit PDF X PDF CDF CDF_INV -0.299105 0.186098 0.218418 -0.299105 0.574842 0.934378 0.956318 0.574842 0.359757 0.99783 0.829509 0.359757 0.0618531 0.788954 0.561695 0.0618531 -0.0851032 0.577115 0.415307 -0.0851032 -0.525341 -0.262184 0.0661187 -0.525341 -0.253093 0.275599 0.257578 -0.253093 -0.447402 -0.109188 0.109957 -0.447402 -0.574484 -0.355613 0.043829 -0.574484 0.135623 0.87071 0.633966 0.135623 ANGLIT_CDF_TEST Normal end of execution. ANGLIT_SAMPLE_TEST Python version: 3.6.5 ANGLIT_MEAN computes the Anglit mean ANGLIT_SAMPLE samples the Anglit distribution ANGLIT_VARIANCE computes the Anglit variance. PDF mean = 0 PDF variance = 0.11685 Sample size = 1000 Sample mean = 0.00239765 Sample variance = 0.116844 Sample maximum = 0.739647 Sample minimum = -0.742509 ANGLIT_SAMPLE_TEST Normal end of execution. ARCSIN_CDF_TEST Python version: 3.6.5 ARCSIN_CDF evaluates the Arcsin CDF ARCSIN_CDF_INV inverts the Arcsin CDF. ARCSIN_PDF evaluates the Arcsin PDF PDF parameter A = 1 X PDF CDF CDF_INV -0.773671 0.502393 0.218418 -0.773671 0.990598 2.32679 0.956318 0.990598 0.859956 0.623687 0.829509 0.859956 0.192611 0.324384 0.561695 0.192611 -0.262942 0.329919 0.415307 -0.262942 -0.978504 1.54349 0.0661187 -0.978504 -0.690074 0.439813 0.257578 -0.690074 -0.940927 0.940048 0.109957 -0.940927 -0.990535 2.31906 0.043829 -0.990535 0.408551 0.348743 0.633966 0.408551 ARCSIN_CDF_TEST Normal end of execution. ARCSIN_SAMPLE_TEST Python version: 3.6.5 ARCSIN_MEAN computes the Arcsin mean ARCSIN_SAMPLE samples the Arcsin distribution ARCSIN_VARIANCE computes the Arcsin variance. PDF parameter A = 1 PDF mean = 0 PDF variance = 0.5 Sample size = 1000 Sample mean = 0.00986339 Sample variance = 0.490326 Sample maximum = 0.999978 Sample minimum = -0.999983 PDF parameter A = 16 PDF mean = 0 PDF variance = 128 Sample size = 1000 Sample mean = -0.453245 Sample variance = 129.51 Sample maximum = 15.9995 Sample minimum = -15.9993 ARCSIN_SAMPLE_TEST Normal end of execution. BENFORD_CDF_TEST Python version: 3.6.5 BENFORD_CDF evaluates the Benford CDF. N CDF(N) CDF(N) by summing 1 0.30103 0.30103 2 0.477121 0.477121 3 0.60206 0.60206 4 0.69897 0.69897 5 0.778151 0.778151 6 0.845098 0.845098 7 0.90309 0.90309 8 0.954243 0.954243 9 1 1 N CDF(N) CDF(N) by summing 10 0.0413927 0.0413927 11 0.0791812 0.0791812 12 0.113943 0.113943 13 0.146128 0.146128 14 0.176091 0.176091 15 0.20412 0.20412 16 0.230449 0.230449 17 0.255273 0.255273 18 0.278754 0.278754 19 0.30103 0.30103 20 0.322219 0.322219 21 0.342423 0.342423 22 0.361728 0.361728 23 0.380211 0.380211 24 0.39794 0.39794 25 0.414973 0.414973 26 0.431364 0.431364 27 0.447158 0.447158 28 0.462398 0.462398 29 0.477121 0.477121 30 0.491362 0.491362 31 0.50515 0.50515 32 0.518514 0.518514 33 0.531479 0.531479 34 0.544068 0.544068 35 0.556303 0.556303 36 0.568202 0.568202 37 0.579784 0.579784 38 0.591065 0.591065 39 0.60206 0.60206 40 0.612784 0.612784 41 0.623249 0.623249 42 0.633468 0.633468 43 0.643453 0.643453 44 0.653213 0.653213 45 0.662758 0.662758 46 0.672098 0.672098 47 0.681241 0.681241 48 0.690196 0.690196 49 0.69897 0.69897 50 0.70757 0.70757 51 0.716003 0.716003 52 0.724276 0.724276 53 0.732394 0.732394 54 0.740363 0.740363 55 0.748188 0.748188 56 0.755875 0.755875 57 0.763428 0.763428 58 0.770852 0.770852 59 0.778151 0.778151 60 0.78533 0.78533 61 0.792392 0.792392 62 0.799341 0.799341 63 0.80618 0.80618 64 0.812913 0.812913 65 0.819544 0.819544 66 0.826075 0.826075 67 0.832509 0.832509 68 0.838849 0.838849 69 0.845098 0.845098 70 0.851258 0.851258 71 0.857332 0.857332 72 0.863323 0.863323 73 0.869232 0.869232 74 0.875061 0.875061 75 0.880814 0.880814 76 0.886491 0.886491 77 0.892095 0.892095 78 0.897627 0.897627 79 0.90309 0.90309 80 0.908485 0.908485 81 0.913814 0.913814 82 0.919078 0.919078 83 0.924279 0.924279 84 0.929419 0.929419 85 0.934498 0.934498 86 0.939519 0.939519 87 0.944483 0.944483 88 0.94939 0.94939 89 0.954243 0.954243 90 0.959041 0.959041 91 0.963788 0.963788 92 0.968483 0.968483 93 0.973128 0.973128 94 0.977724 0.977724 95 0.982271 0.982271 96 0.986772 0.986772 97 0.991226 0.991226 98 0.995635 0.995635 99 1 1 BENFORD_CDF_TEST Normal end of execution. BENFORD_PDF_TEST Python version: 3.6.5 BENFORD_PDF evaluates the Benford PDF. N PDF(N) 1 0.30103 2 0.176091 3 0.124939 4 0.09691 5 0.0791812 6 0.0669468 7 0.0579919 8 0.0511525 9 0.0457575 N PDF(N) 10 0.0413927 11 0.0377886 12 0.0347621 13 0.0321847 14 0.0299632 15 0.0280287 16 0.0263289 17 0.0248236 18 0.0234811 19 0.0222764 20 0.0211893 21 0.0202034 22 0.0193052 23 0.0184834 24 0.0177288 25 0.0170333 26 0.0163904 27 0.0157943 28 0.01524 29 0.0147233 30 0.0142404 31 0.0137883 32 0.013364 33 0.012965 34 0.0125891 35 0.0122345 36 0.0118992 37 0.0115819 38 0.011281 39 0.0109954 40 0.0107239 41 0.0104654 42 0.0102192 43 0.00998422 44 0.00975984 45 0.00954532 46 0.00934003 47 0.00914338 48 0.00895484 49 0.00877392 50 0.00860017 51 0.00843317 52 0.00827253 53 0.00811789 54 0.00796893 55 0.00782534 56 0.00768683 57 0.00755314 58 0.00742402 59 0.00729924 60 0.00717858 61 0.00706185 62 0.00694886 63 0.00683942 64 0.00673338 65 0.00663058 66 0.00653087 67 0.00643411 68 0.00634018 69 0.00624895 70 0.00616031 71 0.00607415 72 0.00599036 73 0.00590886 74 0.00582954 75 0.00575233 76 0.00567713 77 0.00560388 78 0.00553249 79 0.0054629 80 0.00539503 81 0.00532883 82 0.00526424 83 0.00520119 84 0.00513964 85 0.00507953 86 0.0050208 87 0.00496342 88 0.00490733 89 0.0048525 90 0.00479888 91 0.00474644 92 0.00469512 93 0.00464491 94 0.00459575 95 0.00454763 96 0.0045005 97 0.00445434 98 0.00440912 99 0.00436481 BENFORD_PDF_TEST Normal end of execution. BERNOULLI_CDF_TEST Python version: 3.6.5 BERNOULLI_CDF evaluates the Bernoulli CDF BERNOULLI_CDF_INV inverts the Bernoulli CDF. BERNOULLI_PDF evaluates the Bernoulli PDF PDF parameter A = 0.75 X PDF CDF CDF_INV 0 0.25 0.25 0 1 0.75 1 1 1 0.75 1 1 1 0.75 1 1 1 0.75 1 1 0 0.25 0.25 0 1 0.75 1 1 0 0.25 0.25 0 0 0.25 0.25 0 1 0.75 1 1 BERNOULLI_CDF_TEST Normal end of execution. BERNOULLI_SAMPLE_TEST Python version: 3.6.5 BERNOULLI_MEAN computes the Bernoulli mean BERNOULLI_SAMPLE samples the Bernoulli distribution BERNOULLI_VARIANCE computes the Bernoulli variance. PDF parameter A = 0.75 PDF mean = 0.75 PDF variance = 0.1875 Sample size = 1000 Sample mean = 0.768 Sample variance = 0.178354 Sample maximum = 1 Sample minimum = 0 BERNOULLI_SAMPLE_TEST Normal end of execution. BESSEL_I0_TEST: Python version: 3.6.5 BESSEL_I0 evaluates the Bessel function I0(X) X Exact F I0(X) 0 1 1 0.2 1.010025027795146 1.010025027795146 0.4 1.040401782229341 1.040401782229341 0.6 1.09204536431734 1.092045364317339 0.8 1.166514922869803 1.166514922869803 1 1.266065877752008 1.266065877752008 1.2 1.393725584134064 1.393725584134064 1.4 1.553395099731217 1.553395099731216 1.6 1.749980639738909 1.749980639738909 1.8 1.989559356618051 1.989559356618051 2 2.279585302336067 2.279585302336067 2.5 3.289839144050123 3.289839144050123 3 4.880792585865024 4.880792585865024 3.5 7.37820343222548 7.37820343222548 4 11.30192195213633 11.30192195213633 4.5 17.48117185560928 17.48117185560928 5 27.23987182360445 27.23987182360445 6 67.23440697647798 67.23440697647796 8 427.5641157218048 427.5641157218047 10 2815.716628466254 2815.716628466254 BESSEL_I0_TEST Normal end of execution. BESSEL_I0_VALUES_TEST: Python version: 3.6.5 BESSEL_I0_VALUES stores values of the Bessel I function. of order 0. X I(0,X) 0.000000 1 0.200000 1.010025027795146 0.400000 1.040401782229341 0.600000 1.09204536431734 0.800000 1.166514922869803 1.000000 1.266065877752008 1.200000 1.393725584134064 1.400000 1.553395099731217 1.600000 1.749980639738909 1.800000 1.989559356618051 2.000000 2.279585302336067 2.500000 3.289839144050123 3.000000 4.880792585865024 3.500000 7.37820343222548 4.000000 11.30192195213633 4.500000 17.48117185560928 5.000000 27.23987182360445 6.000000 67.23440697647798 8.000000 427.5641157218048 10.000000 2815.716628466254 BESSEL_I0_VALUES_TEST: Normal end of execution. BESSEL_I1_TEST: Python version: 3.6.5 BESSEL_I1 evaluates the Bessel function I1(X) X Exact F I1(X) 0.000000 0 0 0.200000 0.1005008340281251 0.1005008340281251 0.400000 0.2040267557335706 0.2040267557335706 0.600000 0.3137040256049221 0.3137040256049221 0.800000 0.4328648026206398 0.4328648026206398 1.000000 0.565159103992485 0.5651591039924849 1.200000 0.7146779415526431 0.7146779415526432 1.400000 0.8860919814143274 0.8860919814143273 1.600000 1.08481063512988 1.08481063512988 1.800000 1.317167230391899 1.317167230391899 2.000000 1.590636854637329 1.590636854637329 2.500000 2.516716245288698 2.516716245288698 3.000000 3.953370217402609 3.953370217402608 3.500000 6.205834922258365 6.205834922258364 4.000000 9.759465153704451 9.759465153704447 4.500000 15.38922275373592 15.38922275373592 5.000000 24.33564214245053 24.33564214245052 6.000000 61.34193677764024 61.34193677764024 8.000000 399.8731367825601 399.8731367825602 10.000000 2670.988303701255 2670.988303701254 BESSEL_I1_TEST Normal end of execution. BESSEL_I1_VALUES_TEST: Python version: 3.6.5 BESSEL_I1_VALUES stores values of the Bessel I function. of order 1. X I(1,X) 0.000000 0 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.000000 0.565159103992485 1.200000 0.7146779415526431 1.400000 0.8860919814143274 1.600000 1.08481063512988 1.800000 1.317167230391899 2.000000 1.590636854637329 2.500000 2.516716245288698 3.000000 3.953370217402609 3.500000 6.205834922258365 4.000000 9.759465153704451 4.500000 15.38922275373592 5.000000 24.33564214245053 6.000000 61.34193677764024 8.000000 399.8731367825601 10.000000 2670.988303701255 BESSEL_I1_VALUES_TEST: Normal end of execution. BETA_BINOMIAL_CDF_TEST Python version: 3.6.5 BETA_BINOMIAL_CDF evaluates the Beta Binomial CDF BETA_BINOMIAL_CDF_INV inverts the Beta Binomial CDF. BETA_BINOMIAL_PDF evaluates the Beta Binomial PDF PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 X PDF CDF CDF_INV 1 0.285714 0.5 1 4 0.0714286 1 4 3 0.171429 0.928571 3 2 0.257143 0.757143 2 1 0.285714 0.5 1 0 0.214286 0.214286 0 1 0.285714 0.5 1 0 0.214286 0.214286 0 0 0.214286 0.214286 0 2 0.257143 0.757143 2 BETA_BINOMIAL_CDF_TEST Normal end of execution. BETA_BINOMIAL_SAMPLE_TEST Python version: 3.6.5 BETA_BINOMIAL_MEAN computes the Beta Binomial mean BETA_BINOMIAL_SAMPLE samples the Beta Binomial distribution BETA_BINOMIAL_VARIANCE computes the Beta Binomial variance. PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 PDF mean = 1.6 PDF variance = 1.44 Sample size = 1000 Sample mean = 1.62 Sample variance = 1.401 Sample maximum = 4 Sample minimum = 0 BETA_BINOMIAL_SAMPLE_TEST Normal end of execution. BETA_CDF_TEST Python version: 3.6.5 BETA_CDF evaluates the Beta CDF BETA_CDF_INV inverts the Beta CDF. BETA_PDF evaluates the Beta PDF PDF parameter A = 12 PDF parameter B = 12 A B X PDF CDF CDF_INV 12 12 0.678986 0.855881 0.963719 0.678986 12 12 0.401338 2.49915 0.166966 0.401338 12 12 0.635316 1.67553 0.909423 0.635316 12 12 0.594216 2.59905 0.821699 0.594216 12 12 0.504229 3.86528 0.516356 0.504229 12 12 0.802574 0.0256424 0.999472 0.802574 12 12 0.544908 3.53858 0.668704 0.544908 12 12 0.649115 1.38847 0.930537 0.649115 12 12 0.568142 3.14746 0.746604 0.568142 12 12 0.415317 2.80857 0.204083 0.415317 BETA_CDF_TEST Normal end of execution. BETA_CDF_VALUES_TEST: Python version: 3.6.5 BETA_CDF_VALUES stores values of the BETA function. A B X BETA_CDF(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 BETA_CDF_VALUES_TEST: Normal end of execution. BETA_INC_TEST: Python version: 3.6.5 BETA_INC evaluates the normalized incomplete Beta function BETA_INC(A,B,X). A B X Exact F BETA_INC(A,B,X) 0.5 0.5 0.01 0.0637686 0.0637686 0.5 0.5 0.1 0.204833 0.204833 0.5 0.5 1 1 1 1 0.5 0 0 0 1 0.5 0.01 0.00501256 0.00501256 1 0.5 0.1 0.0513167 0.0513167 1 0.5 0.5 0.292893 0.292893 1 1 0.5 0.5 0.5 2 2 0.1 0.028 0.028 2 2 0.2 0.104 0.104 2 2 0.3 0.216 0.216 2 2 0.4 0.352 0.352 2 2 0.5 0.5 0.5 2 2 0.6 0.648 0.648 2 2 0.7 0.784 0.784 2 2 0.8 0.896 0.896 2 2 0.9 0.972 0.972 5.5 5 0.5 0.436191 0.436191 10 0.5 0.9 0.151641 0.151641 10 5 0.5 0.0897827 0.0897827 10 5 1 1 1 10 10 0.5 0.5 0.5 20 5 0.8 0.459877 0.459877 20 10 0.6 0.214682 0.214682 20 10 0.8 0.950736 0.950736 20 20 0.5 0.5 0.5 20 20 0.6 0.897941 0.897941 30 10 0.7 0.22413 0.22413 30 10 0.8 0.758641 0.758641 40 20 0.7 0.700178 0.700178 1 0.5 0.1 0.0513167 0.0513167 1 0.5 0.2 0.105573 0.105573 1 0.5 0.3 0.16334 0.16334 1 0.5 0.4 0.225403 0.225403 1 2 0.2 0.36 0.36 1 3 0.2 0.488 0.488 1 4 0.2 0.5904 0.5904 1 5 0.2 0.67232 0.67232 2 2 0.3 0.216 0.216 3 2 0.3 0.0837 0.0837 4 2 0.3 0.03078 0.03078 5 2 0.3 0.010935 0.010935 1.30625 11.7562 0.225609 0.918885 0.918885 1.30625 11.7562 0.0335568 0.21053 0.21053 1.30625 11.7562 0.0295222 0.182413 0.182413 BETA_INC_TEST Normal end of execution. BETA_INC_VALUES_TEST: Python version: 3.6.5 BETA_INC_VALUES stores values of the BETA function. A B X BETA_INC(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 BETA_INC_VALUES_TEST: Normal end of execution. BETA_SAMPLE_TEST Python version: 3.6.5 BETA_MEAN computes the Beta mean BETA_SAMPLE samples the Beta distribution BETA_VARIANCE computes the Beta variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 0.4 PDF variance = 0.04 Sample size = 1000 Sample mean = 0.406579 Sample variance = 0.0410724 Sample maximum = 0.942944 Sample minimum = 0.00629773 BETA_SAMPLE_TEST Normal end of execution. BETA_VALUES_TEST: Python version: 3.6.5 BETA_VALUES stores values of the BETA function. X Y BETA(X,Y) 0.200000 1.000000 5 0.400000 1.000000 2.5 0.600000 1.000000 1.666666666666667 0.800000 1.000000 1.25 1.000000 0.200000 5 1.000000 0.400000 2.5 1.000000 1.000000 1 2.000000 2.000000 0.1666666666666667 3.000000 3.000000 0.03333333333333333 4.000000 4.000000 0.007142857142857143 5.000000 5.000000 0.001587301587301587 6.000000 2.000000 0.02380952380952381 6.000000 3.000000 0.005952380952380952 6.000000 4.000000 0.001984126984126984 6.000000 5.000000 0.0007936507936507937 6.000000 6.000000 0.0003607503607503608 7.000000 7.000000 8.325008325008325e-05 BETA_VALUES_TEST: Normal end of execution. BINOMIAL_CDF_TEST Python version: 3.6.5 BINOMIAL_CDF evaluates the Binomial CDF BINOMIAL_CDF_INV inverts the Binomial CDF. BINOMIAL_PDF evaluates the Binomial PDF PDF parameter A = 5 PDF parameter B = 0.65 X PDF CDF CDF_INV 3 0.336416 0.571585 3 5 0.116029 1 5 3 0.336416 0.571585 3 4 0.312386 0.883971 4 3 0.336416 0.571585 3 3 0.336416 0.571585 3 2 0.181147 0.235169 2 4 0.312386 0.883971 4 5 0.116029 1 5 2 0.181147 0.235169 2 BINOMIAL_CDF_TEST Normal end of execution. BINOMIAL_SAMPLE_TEST Python version: 3.6.5 BINOMIAL_MEAN computes the Binomial mean BINOMIAL_SAMPLE samples the Binomial distribution BINOMIAL_VARIANCE computes the Binomial variance. PDF parameter A = 5 PDF parameter B = 0.3 PDF mean = 1.5 PDF variance = 1.05 Sample size = 1000 Sample mean = 1.522 Sample variance = 1.02854 Sample maximum = 5 Sample minimum = 0 BINOMIAL_SAMPLE_TEST Normal end of execution. BIRTHDAY_CDF_TEST Python version: 3.6.5 BIRTHDAY_CDF evaluates the Birthday CDF BIRTHDAY_CDF_INV inverts the Birthday CDF. BIRTHDAY_PDF evaluates the Birthday PDF N PDF CDF CDF_INV 1 0 0 1 2 0.00273973 0.00273973 2 3 0.00546444 0.00820417 3 4 0.00815175 0.0163559 4 5 0.0107797 0.0271356 5 6 0.0133269 0.0404625 6 7 0.0157732 0.0562357 7 8 0.0180996 0.0743353 8 9 0.0202885 0.0946238 9 10 0.0223243 0.116948 10 11 0.0241932 0.141141 11 12 0.0258834 0.167025 12 13 0.0273855 0.19441 13 14 0.0286922 0.223103 14 15 0.0297988 0.252901 15 16 0.0307027 0.283604 16 17 0.0314037 0.315008 17 18 0.0319038 0.346911 18 19 0.0322071 0.379119 19 20 0.0323199 0.411438 20 21 0.03225 0.443688 21 22 0.032007 0.475695 22 23 0.0316019 0.507297 23 24 0.031047 0.538344 24 25 0.0303554 0.5687 25 26 0.0295411 0.598241 26 27 0.0286185 0.626859 27 28 0.0276022 0.654461 28 29 0.0265071 0.680969 29 30 0.0253477 0.706316 30 BIRTHDAY_CDF_TEST Normal end of execution. BIRTHDAY_SAMPLE_TEST Python version: 3.6.5 BIRTHDAY_SAMPLE samples the Birthday distribution. N Mean PDF 10 0.027 0.0223243 11 0.023 0.0241932 12 0.026 0.0258834 13 0.026 0.0273855 14 0.029 0.0286922 15 0.029 0.0297988 16 0.031 0.0307027 17 0.032 0.0314037 18 0.026 0.0319038 19 0.028 0.0322071 20 0.039 0.0323199 21 0.029 0.03225 22 0.034 0.032007 23 0.028 0.0316019 24 0.037 0.031047 25 0.041 0.0303554 26 0.029 0.0295411 27 0.028 0.0286185 28 0.033 0.0276022 29 0.031 0.0265071 30 0.022 0.0253477 31 0.023 0.0241384 32 0.02 0.0228929 33 0.018 0.0216243 34 0.024 0.020345 35 0.02 0.0190664 36 0.02 0.0177989 37 0.024 0.0165519 38 0.011 0.0153338 39 0.017 0.0141518 40 0.012 0.0130121 BIRTHDAY_SAMPLE_TEST Normal end of execution. BRADFORD_CDF_TEST Python version: 3.6.5 BRADFORD_CDF evaluates the Bradford CDF BRADFORD_CDF_INV inverts the Bradford CDF. BRADFORD_PDF evaluates the Bradford PDF PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 1.11788 1.59869 0.218418 1.11788 1.92165 0.574785 0.956318 1.92165 1.71934 0.685254 0.829509 1.71934 1.39286 0.993325 0.561695 1.39286 1.25948 1.21682 0.415307 1.25948 1.032 1.97451 0.0661187 1.032 1.14305 1.51422 0.257578 1.14305 1.05489 1.85808 0.109957 1.05489 1.02088 2.03647 0.043829 1.02088 1.46939 0.898629 0.633966 1.46939 BRADFORD_CDF_TEST Normal end of execution. BRADFORD_SAMPLE_TEST Python version: 3.6.5 BRADFORD_MEAN computes the Bradford mean BRADFORD_SAMPLE samples the Bradford distribution BRADFORD_VARIANCE computes the Bradford variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 1.38801 PDF variance = 0.0807807 Sample size = 1000 Sample mean = 1.3901 Sample variance = 0.0795644 Sample maximum = 1.99614 Sample minimum = 1.00085 BRADFORD_SAMPLE_TEST Normal end of execution. BUFFON_BOX_PDF_TEST Python version: 3.6.5 BUFFON_BOX_PDF evaluates the Buffon-Laplace PDF, the probability that, on a grid of cells of width A and height B, a needle of length L, dropped at random, will cross at least one grid line. A B L PDF 1 1 0 0 1 1 0.2 0.241916 1 1 0.4 0.458366 1 1 0.6 0.649352 1 1 0.8 0.814873 1 1 1 0.95493 1 2 0 0 1 2 0.2 0.18462 1 2 0.4 0.356507 1 2 0.6 0.515662 1 2 0.8 0.662085 1 2 1 0.795775 1 3 0 0 1 3 0.2 0.165521 1 3 0.4 0.322554 1 3 0.6 0.471099 1 3 0.8 0.611155 1 3 1 0.742723 1 4 0 0 1 4 0.2 0.155972 1 4 0.4 0.305577 1 4 0.6 0.448817 1 4 0.8 0.58569 1 4 1 0.716197 1 5 0 0 1 5 0.2 0.150242 1 5 0.4 0.295392 1 5 0.6 0.435448 1 5 0.8 0.570411 1 5 1 0.700282 2 1 0 0 2 1 0.2 0.18462 2 1 0.4 0.356507 2 1 0.6 0.515662 2 1 0.8 0.662085 2 1 1 0.795775 2 2 0 0 2 2 0.4 0.241916 2 2 0.8 0.458366 2 2 1.2 0.649352 2 2 1.6 0.814873 2 2 2 0.95493 2 3 0 0 2 3 0.4 0.203718 2 3 0.8 0.39046 2 3 1.2 0.560225 2 3 1.6 0.713014 2 3 2 0.848826 2 4 0 0 2 4 0.4 0.18462 2 4 0.8 0.356507 2 4 1.2 0.515662 2 4 1.6 0.662085 2 4 2 0.795775 2 5 0 0 2 5 0.4 0.173161 2 5 0.8 0.336135 2 5 1.2 0.488924 2 5 1.6 0.631527 2 5 2 0.763944 3 1 0 0 3 1 0.2 0.165521 3 1 0.4 0.322554 3 1 0.6 0.471099 3 1 0.8 0.611155 3 1 1 0.742723 3 2 0 0 3 2 0.4 0.203718 3 2 0.8 0.39046 3 2 1.2 0.560225 3 2 1.6 0.713014 3 2 2 0.848826 3 3 0 0 3 3 0.6 0.241916 3 3 1.2 0.458366 3 3 1.8 0.649352 3 3 2.4 0.814873 3 3 3 0.95493 3 4 0 0 3 4 0.6 0.213268 3 4 1.2 0.407437 3 4 1.8 0.582507 3 4 2.4 0.738479 3 4 3 0.875352 3 5 0 0 3 5 0.6 0.196079 3 5 1.2 0.376879 3 5 1.8 0.5424 3 5 2.4 0.692642 3 5 3 0.827606 4 1 0 0 4 1 0.2 0.155972 4 1 0.4 0.305577 4 1 0.6 0.448817 4 1 0.8 0.58569 4 1 1 0.716197 4 2 0 0 4 2 0.4 0.18462 4 2 0.8 0.356507 4 2 1.2 0.515662 4 2 1.6 0.662085 4 2 2 0.795775 4 3 0 0 4 3 0.6 0.213268 4 3 1.2 0.407437 4 3 1.8 0.582507 4 3 2.4 0.738479 4 3 3 0.875352 4 4 0 0 4 4 0.8 0.241916 4 4 1.6 0.458366 4 4 2.4 0.649352 4 4 3.2 0.814873 4 4 4 0.95493 4 5 0 0 4 5 0.8 0.218997 4 5 1.6 0.417623 4 5 2.4 0.595876 4 5 3.2 0.753758 4 5 4 0.891268 5 1 0 0 5 1 0.2 0.150242 5 1 0.4 0.295392 5 1 0.6 0.435448 5 1 0.8 0.570411 5 1 1 0.700282 5 2 0 0 5 2 0.4 0.173161 5 2 0.8 0.336135 5 2 1.2 0.488924 5 2 1.6 0.631527 5 2 2 0.763944 5 3 0 0 5 3 0.6 0.196079 5 3 1.2 0.376879 5 3 1.8 0.5424 5 3 2.4 0.692642 5 3 3 0.827606 5 4 0 0 5 4 0.8 0.218997 5 4 1.6 0.417623 5 4 2.4 0.595876 5 4 3.2 0.753758 5 4 4 0.891268 5 5 0 0 5 5 1 0.241916 5 5 2 0.458366 5 5 3 0.649352 5 5 4 0.814873 5 5 5 0.95493 BUFFON_BOX_PDF_TEST Normal end of execution. BUFFON_BOX_SAMPLE_TEST Python version: 3.6.5 BUFFON_BOX_SAMPLE simulates a Buffon-Laplace needle dropping experiment. On a grid of cells of width A and height B a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1 Cell height B = 1 Needle length L = 1 Trials Hits Est(Pi) Err 10 9 3.33333 0.191741 100 97 3.09278 0.0488091 10000 9529 3.14828 0.00669153 1000000 955057 3.14117 0.000418881 BUFFON_BOX_SAMPLE_TEST Normal end of execution. BUFFON_PDF_TEST Python version: 3.6.5 BUFFON_PDF evaluates the Buffon PDF, the probability that, on a grid of cells of width A, a needle of length L, dropped at random, will cross at least one grid line. A L PDF 1 0 0 1 0.2 0.127324 1 0.4 0.254648 1 0.6 0.381972 1 0.8 0.509296 1 1 0.63662 2 0 0 2 0.4 0.127324 2 0.8 0.254648 2 1.2 0.381972 2 1.6 0.509296 2 2 0.63662 3 0 0 3 0.6 0.127324 3 1.2 0.254648 3 1.8 0.381972 3 2.4 0.509296 3 3 0.63662 4 0 0 4 0.8 0.127324 4 1.6 0.254648 4 2.4 0.381972 4 3.2 0.509296 4 4 0.63662 5 0 0 5 1 0.127324 5 2 0.254648 5 3 0.381972 5 4 0.509296 5 5 0.63662 BUFFON_PDF_TEST Normal end of execution. BUFFON_SAMPLE_TEST Python version: 3.6.5 BUFFON_SAMPLE simulates a Buffon-Laplace needle dropping experiment. On a grid of cells of width A, a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1 Needle length L = 1 Trials Hits Est(Pi) Err 10 8 2.5 0.641593 100 63 3.1746 0.0330105 10000 6327 3.16106 0.0194631 1000000 636344 3.14295 0.00136147 BUFFON_SAMPLE_TEST Normal end of execution. BURR_CDF_TEST Python version: 3.6.5 BURR_CDF evaluates the Burr CDF BURR_CDF_INV inverts the Burr CDF. BURR_PDF evaluates the Burr PDF PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF parameter D = 2 X PDF CDF CDF_INV 2.01609 0.53504 0.218418 2.01609 4.11676 0.0665164 0.956318 4.11676 3.24896 0.267041 0.829509 3.24896 2.5984 0.55603 0.561695 2.5984 2.35035 0.611426 0.415307 2.35035 1.65293 0.288558 0.0661187 1.65293 2.08707 0.566965 0.257578 2.08707 1.78285 0.385956 0.109957 1.78285 1.56598 0.224626 0.043829 1.56598 2.73503 0.499984 0.633966 2.73503 BURR_DF_TEST Normal end of execution. BURR_SAMPLE_TEST Python version: 3.6.5 BURR_MEAN computes the Burr mean BURR_VARIANCE computes the Burr variance BURR_SAMPLE Burr samples the distribution PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF parameter D = 2 PDF mean = 2.61227 PDF variance = 0.62513 Sample size = 1000 Sample mean = 2.614142 Sample variance = 0.605821 Sample maximum = 6.506014 Sample minimum = 1.194550 BURR_SAMPLE_TEST Normal end of execution. CARDIOID_CDF_TEST Python version: 3.6.5 CARDIOID_CDF evaluates the Cardioid CDF CARDIOID_CDF_INV inverts the Cardioid CDF. CARDIOID_PDF evaluates the Cardioid PDF PDF parameter A = 0 PDF parameter B = 0.25 X PDF CDF CDF_INV -1.28896 0.181287 0.218419 -1.28895 2.61646 0.0902998 0.956317 2.61646 1.57037 0.159189 0.829509 1.57037 0.259396 0.23607 0.561695 0.259396 -0.357278 0.233707 0.415307 -0.357278 -2.38175 0.101466 0.0661188 -2.38175 -1.08178 0.196537 0.257578 -1.08178 -1.99504 0.126398 0.109957 -1.99504 -2.61484 0.0903646 0.0438293 -2.61484 0.571348 0.226093 0.633966 0.571348 CARDIOID_CDF_TEST Normal end of execution. CARDIOID_SAMPLE_TEST Python version: 3.6.5 CARDIOID_MEAN computes the Cardioid mean CARDIOID_SAMPLE samples the Cardioid distribution CARDIOID_VARIANCE computes the Cardioid variance. PDF parameter A = 0 PDF parameter B = 0.25 PDF mean = 0 PDF variance = 0 Sample size = 1000 Sample mean = 0.00991354 Sample variance = 2.28985 Sample maximum = 3.11531 Sample minimum = -3.11849 CARDIOID_SAMPLE_TEST Normal end of execution. CAUCHY_CDF_TEST Python version: 3.6.5 CAUCHY_CDF evaluates the Cauchy CDF CAUCHY_CDF_INV inverts the Cauchy CDF. CAUCHY_PDF evaluates the Cauchy PDF PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV -1.66329 0.0425934 0.218418 -1.66329 23.7233 0.0019857 0.956318 23.7233 7.05492 0.0276373 0.829509 7.05492 2.58886 0.102167 0.561695 2.58886 1.1824 0.0987675 0.415307 1.1824 -12.2343 0.00451256 0.0661187 -12.2343 -0.860458 0.0555766 0.257578 -0.860458 -6.33637 0.0121655 0.109957 -6.33637 -19.6498 0.00199897 0.043829 -19.6498 3.34283 0.0883932 0.633966 3.34283 CAUCHY_CDF_TEST Normal end of execution. CAUCHY_SAMPLE_TEST Python version: 3.6.5 CAUCHY_MEAN computes the Cauchy mean CAUCHY_VARIANCE computes the Cauchy variance CAUCHY_SAMPLE samples the Cauchy distribution. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 1.79769e+308 Sample size = 1000 Sample mean = 1.66442 Sample variance = 1579.41 Sample maximum = 458.532 Sample minimum = -517.438 CAUCHY_SAMPLE_TEST Normal end of execution. CHEBYSHEV1_CDF_TEST Python version: 3.6.5 CHEBYSHEV1_CDF evaluates the Chebyshev1 CDF CHEBYSHEV1_CDF_INV inverts the Chebyshev1 CDF. CHEBYSHEV1_PDF evaluates the Chebyshev1 PDF X PDF CDF CDF_INV -0.773671 0.502393 0.218418 -0.773671 0.990598 2.32679 0.956318 0.990598 0.859956 0.623687 0.829509 0.859956 0.192611 0.324384 0.561695 0.192611 -0.262942 0.329919 0.415307 -0.262942 -0.978504 1.54349 0.0661187 -0.978504 -0.690074 0.439813 0.257578 -0.690074 -0.940927 0.940048 0.109957 -0.940927 -0.990535 2.31906 0.043829 -0.990535 0.408551 0.348743 0.633966 0.408551 CHEBYSHEV1_CDF_TEST Normal end of execution. CHEBYSHEV1_SAMPLE_TEST Python version: 3.6.5 CHEBYSHEV1_MEAN computes the Chebyshev1 mean CHEBYSHEV1_SAMPLE samples the Chebyshev1 distribution CHEBYSHEV1_VARIANCE computes the Chebyshev1 variance. PDF mean = 0 PDF variance = 0.5 Sample size = 1000 Sample mean = 0.00986339 Sample variance = 0.490326 Sample maximum = 0.999978 Sample minimum = -0.999983 CHEBYSHEV1_SAMPLE_TEST Normal end of execution. CHI_CDF_TEST Python version: 3.6.5 CHI_CDF evaluates the Chi CDF. CHI_CDF_INV inverts the Chi CDF. CHI_PDF evaluates the Chi PDF. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 5.29456 0.183427 0.797383 5.29492 7.13704 0.0338961 0.975756 7.13672 2.45642 0.162283 0.0878118 2.45703 6.98388 0.040642 0.97006 6.98438 4.74497 0.242317 0.680042 4.74512 3.0281 0.245322 0.205594 3.02832 2.7946 0.214758 0.151764 2.79492 2.95034 0.235816 0.186883 2.9502 2.49461 0.168514 0.0941283 2.49414 2.35125 0.144944 0.0716542 2.35156 CHI_CDF_TEST Normal end of execution. CHI_SAMPLE_TEST Python version: 3.6.5 CHI_MEAN computes the Chi mean CHI_VARIANCE computes the Chi variance CHI_SAMPLE samples the Chi distribution. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 4.19154 PDF variance = 1.81408 Sample size = 1000 Sample mean = 4.15337 Sample variance = 1.9332 Sample maximum = 9.32689 Sample minimum = 1.20601 CHI_SAMPLE_TEST Normal end of execution. CHI_SQUARE_CDF_TEST Python version: 3.6.5 CHI_SQUARE_CDF evaluates the Chi Square CDF CHI_SQUARE_CDF_INV inverts the Chi Square CDF. CHI_SQUARE_PDF evaluates the Chi Square PDF PDF parameter A = 4 X PDF CDF CDF_INV 6.22214 0.0693042 0.183162 1.5551 8.25908 0.0332227 0.0825356 0.948754 9.02741 0.0247301 0.0604179 0.791514 4.13727 0.130694 0.387747 2.68266 0.703353 0.123704 0.950915 9.53243 1.44998 0.175567 0.835464 6.50404 0.634817 0.115542 0.959117 9.97313 8.54272 0.02982 0.0736027 0.887149 13.0901 0.00470332 0.0108438 0.310051 1.46095 0.175928 0.833535 6.47354 CHI_SQUARE_CDF_TEST Normal end of execution. CHI_SQUARE_SAMPLE_TEST Python version: 3.6.5 CHI_SQUARE_MEAN computes the Chi Square mean CHI_SQUARE_SAMPLE samples the Chi Square distribution CHI_SQUARE_VARIANCE computes the Chi Square variance. PDF parameter A = 10 PDF mean = 10 PDF variance = 20 Sample size = 1000 Sample mean = 9.97738 Sample variance = 21.1882 Sample maximum = 31.1387 Sample minimum = 1.63719 CHI_SQUARE_SAMPLE_TEST Normal end of execution. CHI_SQUARE_NONCENTRAL_SAMPLE_TEST Python version: 3.6.5 CHI_SQUARE_NONCENTRAL_MEAN computes the Chi Square Noncentral mean. CHI_SQUARE_NONCENTRAL_SAMPLE samples the Chi Square Noncentral PDF. CHI_SQUARE_NONCENTRAL_VARIANCE computes the Chi Square Noncentral variance. PDF parameter A = 3 PDF parameter B = 2 PDF mean = 5 PDF variance = 14 Initial seed = 123456789 Final seed = 200382020 Sample size = 1000 Sample mean = 4.99931 Sample variance = 13.5745 Sample maximum = 22.5373 Sample minimum = 0.0271069 CHI_SQUARE_NONCENTRAL_SAMPLE_TEST Normal end of execution. CIRCULAR_NORMAL_SAMPLE_TEST Python version: 3.6.5 CIRCULAR_NORMAL_MEAN computes the Circular Normal mean CIRCULAR_NORMAL_SAMPLE samples the Circular Normal distribution CIRCULAR_NORMAL_VARIANCE computes the Circular Normal variance. PDF means = 1 5 PDF variances = 0.5625 0.5625 Sample size = 1000 Sample mean = 1.00436 5.01619 Sample variance = 0.561586 0.565407 Sample maximum = 3.49644 7.2714 Sample minimum = -1.27232 2.82138 CIRCULAR_NORMAL_SAMPLE_TEST Normal end of execution. CIRCULAR_NORMAL_01_SAMPLE_TEST Python version: 3.6.5 CIRCULAR_NORMAL_01_MEAN computes the Circular Normal 01 mean CIRCULAR_NORMAL_01_SAMPLE samples the Circular Normal 01 distribution CIRCULAR_NORMAL_01_VARIANCE computes the Circular Normal 01 variance. PDF means = 0 0 PDF variances = 1 1 Sample size = 1000 Sample mean = 0.00581875 0.0215871 Sample variance = 0.998375 1.00517 Sample maximum = 3.32858 3.02853 Sample minimum = -3.02975 -2.90483 CIRCULAR_NORMAL_01_SAMPLE_TEST Normal end of execution. COSINE_CDF_TEST Python version: 3.6.5 COSINE_CDF evaluates the Cosine CDF. COSINE_CDF_INV inverts the Cosine CDF. COSINE_PDF evaluates the Cosine PDF. PDF parameter A = 2 PDF parameter B = 1 X PDF CDF CDF_INV 1.04663 0.0921411 0.218496 1.04663 3.93128 -0.0561385 0.956298 3.93128 3.15509 0.0642729 0.829438 3.15509 2.19443 0.156156 0.561695 2.19443 1.73232 0.153487 0.415302 1.73232 0.258932 -0.0269689 0.066047 0.258932 1.19619 0.110449 0.257478 1.19619 0.542718 0.0180276 0.109936 0.542718 0.0702522 -0.05591 0.0438598 0.0702522 2.42721 0.144851 0.633937 2.42721 COSINE_CDF_TEST Normal end of execution. COSINE_SAMPLE_TEST Python version: 3.6.5 COSINE_MEAN computes the Cosine mean COSINE_SAMPLE samples the Cosine distribution COSINE_VARIANCE computes the Cosine variance. PDF parameter A = 2 PDF parameter B = 1 PDF mean = 2 PDF variance = 1.28987 Sample size = 1000 Sample mean = 2.00654 Sample variance = 1.29547 Sample maximum = 4.71208 Sample minimum = -0.72435 COSINE_SAMPLE_TEST Normal end of execution. COUPON_SAMPLE_TEST Python version: 3.6.5 COUPON_SAMPLE samples the coupon PDF. Number of coupon types is 5 Expected wait is about 8.04719 0 10 1 8 2 14 3 7 4 10 5 11 6 17 7 11 8 6 9 12 Average wait was 10.6 Number of coupon types is 10 Expected wait is about 23.0259 0 18 1 20 2 23 3 24 4 21 5 29 6 31 7 47 8 42 9 27 Average wait was 28.2 Number of coupon types is 15 Expected wait is about 40.6208 0 64 1 23 2 50 3 81 4 44 5 40 6 48 7 72 8 64 9 31 Average wait was 51.7 Number of coupon types is 20 Expected wait is about 59.9146 0 64 1 87 2 67 3 95 4 67 5 99 6 63 7 82 8 87 9 89 Average wait was 80 Number of coupon types is 25 Expected wait is about 80.4719 0 101 1 82 2 79 3 67 4 93 5 92 6 96 7 91 8 164 9 134 Average wait was 99.9 COUPON_SAMPLE_TEST Normal end of execution. COUPON_COMPLETE_PDF_TEST Python version: 3.6.5 COUPON_COMPLETE_PDF evaluates the Coupon Complete PDF. Number of coupon types is 2 BOX_NUM PDF CDF 1 0 0 2 0.5 0.5 3 0.25 0.75 4 0.125 0.875 5 0.0625 0.9375 6 0.03125 0.96875 7 0.015625 0.984375 8 0.0078125 0.992188 9 0.00390625 0.996094 10 0.00195312 0.998047 11 0.000976562 0.999023 12 0.000488281 0.999512 13 0.000244141 0.999756 14 0.00012207 0.999878 15 6.10352e-05 0.999939 16 3.05176e-05 0.999969 17 1.52588e-05 0.999985 18 7.62939e-06 0.999992 19 3.8147e-06 0.999996 20 1.90735e-06 0.999998 Number of coupon types is 3 BOX_NUM PDF CDF 1 0 0 2 0 0 3 0.222222 0.222222 4 0.222222 0.444444 5 0.17284 0.617284 6 0.123457 0.740741 7 0.085048 0.825789 8 0.0576132 0.883402 9 0.0387136 0.922116 10 0.0259107 0.948026 11 0.0173077 0.965334 12 0.0115497 0.976884 13 0.00770358 0.984587 14 0.00513698 0.989724 15 0.00342507 0.993149 16 0.00228352 0.995433 17 0.00152239 0.996955 18 0.00101494 0.99797 19 0.000676634 0.998647 20 0.000451091 0.999098 Number of coupon types is 4 BOX_NUM PDF CDF 1 0 0 2 0 0 3 0 0 4 0.09375 0.09375 5 0.140625 0.234375 6 0.146484 0.380859 7 0.131836 0.512695 8 0.110229 0.622925 9 0.0884399 0.711365 10 0.0692368 0.780602 11 0.0533867 0.833988 12 0.040771 0.874759 13 0.0309441 0.905703 14 0.0233911 0.929094 15 0.0176349 0.946729 16 0.0132719 0.960001 17 0.00997682 0.969978 18 0.00749406 0.977472 19 0.00562627 0.983098 20 0.00422256 0.987321 COUPON_COMPLETE_PDF_TEST: Normal end of execution. DERANGED_CDF_TEST Python version: 3.6.5 DERANGED_CDF evaluates the Deranged CDF DERANGED_CDF_INV inverts the Deranged CDF. DERANGED_PDF evaluates the Deranged PDF PDF parameter A = 7 X PDF CDF CDF_INV 0 0.367857 0.367857 0 1 0.368056 0.735913 1 2 0.183333 0.919246 2 3 0.0625 0.981746 3 4 0.0138889 0.995635 4 5 0.00416667 0.999802 5 6 0 0.999802 5 7 0.000198413 1 7 DERANGED_CDF_TEST Normal end of execution. DERANGED_SAMPLE_TEST Python version: 3.6.5 DERANGED_MEAN computes the Deranged mean. DERANGED_VARIANCE computes the Deranged variance. DERANGED_SAMPLE samples the Deranged distribution. PDF parameter A = 7 PDF mean = 1 PDF variance = 1 Sample size = 1000 Sample mean = 1.004 Sample variance = 0.984969 Sample maximum = 5 Sample minimum = 0 DERANGED_SAMPLE_TEST Normal end of execution. DIGAMMA_TEST: Python version: 3.6.5 DIGAMMA computes the Digamma or Psi function. Compare the result to tabulated values. X FX FX2 (Tabulated) (DIGAMMA) DIFF 0.1 -10.42375494041108 -10.42375494041114 5.862e-14 0.2 -5.289039896592188 -5.289039896592243 5.507e-14 0.3 -3.502524222200133 -3.502524222200181 4.796e-14 0.4 -2.561384544585116 -2.561384544585158 4.174e-14 0.5 -1.963510026021423 -1.963510026021564 1.406e-13 0.6 -1.54061921389319 -1.540619213893313 1.232e-13 0.7 -1.220023553697935 -1.220023553698041 1.064e-13 0.8 -0.9650085667061385 -0.9650085667062314 9.281e-14 0.9 -0.7549269499470515 -0.7549269499471327 8.127e-14 1 -0.5772156649015329 -0.5772156649016036 7.072e-14 1.1 -0.4237549404110768 -0.4237549404111393 6.251e-14 1.2 -0.2890398965921883 -0.2890398965922431 5.479e-14 1.3 -0.1691908888667997 -0.1691908888668481 4.841e-14 1.4 -0.06138454458511615 -0.06138454458515841 4.226e-14 1.5 0.03648997397857652 0.03648997397843547 1.411e-13 1.6 0.1260474527734763 0.1260474527733536 1.227e-13 1.7 0.208547874873494 0.2085478748733869 1.071e-13 1.8 0.2849914332938615 0.2849914332937686 9.293e-14 1.9 0.3561841611640597 0.3561841611639783 8.143e-14 2 0.4227843350984671 0.4227843350983961 7.094e-14 DIGAMMA_TEST: Normal end of execution. DIPOLE_CDF_TEST Python version: 3.6.5 DIPOLE_CDF evaluates the Dipole CDF. DIPOLE_CDF_INV inverts the Dipole CDF. DIPOLE_PDF evaluates the Dipole PDF. PDF parameter A = 0 PDF parameter B = 1 X PDF CDF CDF_INV 0.515107 0.573233 0.780988 0.515137 -1.28591 0.153127 0.056141 -1.28516 0.467924 0.589867 0.761502 0.467773 0.295557 0.627128 0.677995 0.29541 -0.16527 0.635573 0.396656 -0.165283 -0.219095 0.63352 0.364799 -0.219238 0.0507089 0.63661 0.532227 0.0507812 0.883735 0.374656 0.888326 0.883789 -0.317761 0.624268 0.310195 -0.317871 0.298513 0.626776 0.679584 0.29834 PDF parameter A = 0.785398 PDF parameter B = 0.5 X PDF CDF CDF_INV 3.54104 0.0257138 0.906512 3.54102 -52.801 0.000113121 0.00599923 -52.8281 1.53702 0.0961276 0.792731 1.53711 1.10007 0.172998 0.72915 1.10059 1.08444 0.176405 0.726317 1.08447 0.272584 0.315787 0.510635 0.272461 -1.33073 0.12762 0.176412 -1.33057 3.42544 0.0268054 0.903338 3.42383 -0.185181 0.317728 0.364776 -0.185059 1.73739 0.0736105 0.813954 1.73779 PDF parameter A = 1.5708 PDF parameter B = 0 X PDF CDF CDF_INV -3.5515 0.0233825 0.0873648 -3.55078 2.44916 0.0454834 0.876609 2.44727 2.26701 0.0518476 0.867763 2.2666 1.20946 0.129247 0.780086 1.20898 0.893235 0.177048 0.732069 0.893555 -3.04762 0.03094 0.100922 -3.04785 -0.0293728 0.318035 0.490653 -0.0292969 86.57 4.24675e-05 0.996323 87.6875 -0.73379 0.206903 0.298495 -0.733398 11.6595 0.00232437 0.972766 11.6172 DIPOLE_CDF_TEST Normal end of execution. DIPOLE_SAMPLE_TEST Python version: 3.6.5 DIPOLE_SAMPLE samples the Dipole distribution. PDF parameter A = 0 PDF parameter B = 1 Sample size = 1000 Sample mean = 0.017141 Sample variance = 0.728062 Sample maximum = 4.78718 Sample minimum = -5.67547 PDF parameter A = 0.785398 PDF parameter B = 0.5 Sample size = 1000 Sample mean = 0.28364 Sample variance = 252.082 Sample maximum = 245.982 Sample minimum = -245.584 PDF parameter A = 1.5708 PDF parameter B = 0 Sample size = 1000 Sample mean = -0.179305 Sample variance = 242.215 Sample maximum = 119.648 Sample minimum = -335.78 DIPOLE_SAMPLE_TEST Normal end of execution. DIRICHLET_PDF_TEST Python version: 3.6.5 DIRICHLET_PDF evaluates the Dirichlet PDF. Number of components N = 3 PDF parameters A: 0: 0.25 1: 0.5 2: 1.25 PDF arguments X: 0: 0.5 1: 0.125 2: 0.375 PDF value = 0.63907 DIRICHLET_PDF_TEST Normal end of execution. DIRICHLET_SAMPLE_TEST Python version: 3.6.5 DIRICHLET_SAMPLE samples the Dirichlet distribution DIRICHLET_MEAN computes the Dirichlet mean DIRICHLET_VARIANCE computes the Dirichlet variance. Number of components N = 3 PDF parameters A: 0: 0.25 1: 0.5 2: 1.25 PDF mean, variance: 0 0.125 0.0364583 1 0.25 0.0625 2 0.625 0.078125 Second moment matrix: Col: 0 1 2 Row 0 : 0.0520833 0.0208333 0.0520833 1 : 0.0208333 0.125 0.104167 2 : 0.0520833 0.104167 0.46875 Sample size = 1000 Observed Min, Max, Mean, Variance: 0 4.0796e-11 0.975128 0.128337 0.0377062 1 1.30377e-06 0.976032 0.23718 0.0592189 2 0.000245466 0.999945 0.634483 0.0751289 DIRICHLET_SAMPLE_TEST Normal end of execution. DIRICHLET_MIX_PDF_TEST Python version: 3.6.5 DIRICHLET_MIX_PDF evaluates the Dirichlet Mix PDF. Number of elements ELEM_NUM = 3 Number of components COMP_NUM = 2 PDF parameters A(ELEM,COMP): Col: 0 1 Row 0 : 0.25 1.5 1 : 0.5 0.5 2 : 1.25 2 Component weights: 0: 1 1: 2 PDF value = 2.12288 DIRICHLET_MIX_PDF_TEST Normal end of execution. DIRICHLET_MIX_SAMPLE_TEST Python version: 3.6.5 DIRICHLET_MIX_SAMPLE samples the Dirichlet Mix distribution DIRICHLET_MIX_MEAN computes the Dirichlet Mix mean Number of elements ELEM_NUM = 3 Number of components COMP_NUM = 2 PDF parameters A(ELEM,COMP): Col: 0 1 Row 0 : 0.25 1.5 1 : 0.5 0.5 2 : 1.25 2 Component weights: 0: 1 1: 2 PDF mean: 0: 0.291667 1: 0.166667 2: 0.541667 Sample size = 1000 Observed Min, Max, Mean, Variance: 0 3.62858e-10 0.986951 0.278716 0.0546592 1 5.84186e-08 0.993637 0.170222 0.0397946 2 0.00518575 0.998934 0.551062 0.062022 DIRICHLET_MIX_SAMPLE_TEST Normal end of execution. DISCRETE_CDF_TEST DISCRETE_CDF evaluates the Discrete CDF DISCRETE_CDF_INV inverts the Discrete CDF. DISCRETE_PDF evaluates the Discrete PDF PDF parameter A = 6 PDF parameters B: 0: 1 1: 2 2: 6 3: 2 4: 4 5: 1 X PDF CDF CDF_INV 3 0.375 0.5625 3 6 0.0625 1 6 5 0.25 0.9375 5 3 0.375 0.5625 3 3 0.375 0.5625 3 2 0.125 0.1875 2 3 0.375 0.5625 3 2 0.125 0.1875 2 1 0.0625 0.0625 1 4 0.125 0.6875 4 DISCRETE_CDF_TEST Normal end of execution. DISCRETE_SAMPLE_TEST DISCRETE_MEAN computes the Discrete mean DISCRETE_SAMPLE samples the Discrete distribution DISCRETE_VARIANCE computes the Discrete variance. PDF parameter A = 6 PDF parameters B: 0: 1 1: 2 2: 6 3: 2 4: 4 5: 1 PDF mean = 3.5625 PDF variance = 1.74609 Sample size = 1000 Sample mean = 3.559 Sample variance = 1.73826 Sample maximum = 6 Sample minimum = 1 DISCRETE_SAMPLE_TEST Normal end of execution. DISK_SAMPLE_TEST DISK_MEAN returns the Disk mean. DISK_SAMPLE samples the Disk distribution. DISK_VARIANCE returns the Disk variance. X coordinate of center is A = 10 Y coordinate of center is B = 4 Radius is C = 5 Disk mean = 10 4 Disk variance = 12.5 Sample size = 1000 Sample mean = 9.99877 4.10057 Sample variance = 12.4472 Sample maximum = 14.8697 8.94495 Sample minimum = 5.07302 -0.940427 DISK_SAMPLE_TEST Normal end of execution. EMPIRICAL_DISCRETE_CDF_TEST Python version: 3.6.5 EMPIRICAL_DISCRETE_CDF evaluates the Empirical Discrete CDF EMPIRICAL_DISCRETE_CDF_INV inverts the Empirical Discrete CDF. EMPIRICAL_DISCRETE_PDF evaluates the Empirical Discrete PDF PDF parameter A = 6 PDF parameter B: 0: 1 1: 1 2: 3 3: 2 4: 1 5: 2 PDF parameter C: 0: 0 1: 1 2: 2 3: 4.5 4: 6 5: 10 X PDF CDF CDF_INV 2 0.3 0.5 2 10 0.2 1 10 10 0.2 1 10 4.5 0.2 0.7 4.5 2 0.3 0.5 2 0 0.1 0.1 0 2 0.3 0.5 2 1 0.1 0.2 1 0 0.1 0.1 0 4.5 0.2 0.7 4.5 EMPIRICAL_DISCRETE_CDF_TEST Normal end of execution. EMPIRICAL_DISCRETE_SAMPLE_TEST Python version: 3.6.5 EMPIRICAL_DISCRETE_MEAN computes the Empirical Discrete mean EMPIRICAL_DISCRETE_SAMPLE samples the Empirical Discrete distribution EMPIRICAL_DISCRETE_VARIANCE computes the Empirical Discrete variance. PDF parameter A = 6 PDF parameter B: 0: 1 1: 1 2: 3 3: 2 4: 1 5: 2 PDF parameter C: 0: 0 1: 1 2: 2 3: 4.5 4: 6 5: 10 PDF mean = 4.2 PDF variance = 11.31 Sample size = 1000 Sample mean = 4.231 Sample variance = 11.2023 Sample maximum = 10 Sample minimum = 0 EMPIRICAL_DISCRETE_SAMPLE_TEST Normal end of execution. ENGLISH_LETTER_CDF_TEST Python version: 3.6.5 ENGLISH_LETTER_CDF evaluates the English Letter CDF ENGLISH_LETTER_CDF_INV inverts the English Letter CDF. ENGLISH_LETTER_PDF evaluates the English Letter PDF C PDF CDF CDF_INV 'e' 0.12702 0.29396 'e' 'w' 0.02361 0.97802 'w' 't' 0.09056 0.91705 't' 'n' 0.06749 0.60804 'n' 'i' 0.06966 0.46699 'i' 'a' 0.08167 0.08167 'a' 'e' 0.12702 0.29396 'e' 'c' 0.02782 0.12441 'c' 'a' 0.08167 0.08167 'a' 'o' 0.07507 0.68311 'o' ENGLISH_LETTER_CDF_TEST Normal end of execution. ENGLISH_SENTENCE_LENGTH_CDF_TEST Python version: 3.6.5 ENGLISH_SENTENCE_LENGTH_CDF evaluates the English Sentence Length CDF ENGLISH_SENTENCE_LENGTH_CDF_INV inverts the English Sentence Length CDF. ENGLISH_SENTENCE_LENGTH_PDF evaluates the English Sentence Length PDF X PDF CDF CDF_INV 9 0.0329364 0.232179 9 43 0.00478109 0.957141 43 30 0.0155962 0.840951 30 19 0.0333674 0.587303 19 14 0.0375972 0.415634 14 5 0.0305008 0.0965039 5 10 0.0354122 0.267591 10 6 0.0319642 0.128468 6 4 0.0255292 0.0660031 4 21 0.0287367 0.647141 21 ENGLISH_SENTENCE_LENGTH_CDF_TEST Normal end of execution. ENGLISH_SENTENCE_LENGTH_SAMPLE_TEST Python version: 3.6.5 ENGLISH_SENTENCE_LENGTH_MEAN computes the English Sentence Length mean ENGLISH_SENTENCE_LENGTH_SAMPLE samples the English Sentence Length distribution ENGLISH_SENTENCE_LENGTH_VARIANCE computes the English Sentence Length variance. PDF mean = 19.1147 PDF variance = 147.443 Sample size = 1000 Sample mean = 19.107 Sample variance = 144.238 Sample maximum = 67 Sample minimum = 1 ENGLISH_SENTENCE_LENGTH_SAMPLE_TEST Normal end of execution. ENGLISH_WORD_LENGTH_CDF_TEST Python version: 3.6.5 ENGLISH_WORD_LENGTH_CDF evaluates the English Word Length CDF ENGLISH_WORD_LENGTH_CDF_INV inverts the English Word Length CDF. ENGLISH_WORD_LENGTH_PDF evaluates the English Word Length PDF X PDF CDF CDF_INV 3 0.211926 0.413282 3 10 0.0276608 0.965289 10 7 0.0772423 0.841075 7 4 0.156785 0.570067 4 4 0.156785 0.570067 4 2 0.169755 0.201356 2 3 0.211926 0.413282 3 2 0.169755 0.201356 2 2 0.169755 0.201356 2 5 0.108523 0.67859 5 ENGLISH_WORD_LENGTH_CDF_TEST Normal end of execution. ENGLISH_WORD_LENGTH_SAMPLE_TEST Python version: 3.6.5 ENGLISH_WORD_LENGTH_MEAN computes the English Word Length mean ENGLISH_WORD_LENGTH_SAMPLE samples the English Word Length distribution ENGLISH_WORD_LENGTH_VARIANCE computes the English Word Length variance. PDF mean = 4.73912 PDF variance = 7.05635 Sample size = 1000 Sample mean = 4.74 Sample variance = 6.96737 Sample maximum = 15 Sample minimum = 1 ENGLISH_WORD_LENGTH_SAMPLE_TEST Normal end of execution. ERLANG_CDF_TEST Python version: 3.6.5 ERLANG_CDF evaluates the Erlang CDF. ERLANG_CDF_INV inverts the Erlang CDF. ERLANG_PDF evaluates the Erlang PDF. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 11.2926 0.0385403 0.887143 11.293 3.85983 0.122337 0.173777 3.85938 1.91828 0.0332989 0.0114788 1.91797 4.33148 0.131139 0.233762 4.33203 8.02827 0.0919195 0.681759 8.02734 6.42343 0.122108 0.50924 6.42383 5.14542 0.135161 0.342996 5.14551 4.9536 0.135317 0.317044 4.95312 6.71621 0.117176 0.544281 6.7168 5.9501 0.128886 0.449771 5.9502 ERLANG_CDF_TEST Normal end of execution. ERLANG_SAMPLE_TEST Python version: 3.6.5 ERLANG_MEAN computes the Erlang mean ERLANG_SAMPLE samples the Erlang distribution ERLANG_VARIANCE computes the Erlang variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 7 PDF variance = 12 Sample size = 1000 Sample mean = 7.00341 Sample variance = 11.491 Sample maximum = 21.5166 Sample minimum = 1.22651 ERLANG_SAMPLE_TEST Normal end of execution. EXPONENTIAL_CDF_TEST Python version: 3.6.5 EXPONENTIAL_CDF evaluates the Exponential CDF. EXPONENTIAL_CDF_INV inverts the Exponential CDF. EXPONENTIAL_PDF evaluates the Exponential PDF. PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV 1.49287 0.390791 0.218418 1.49287 7.26162 0.0218412 0.956318 7.26162 4.53815 0.0852454 0.829509 4.53815 2.64968 0.219152 0.561695 2.64968 2.07334 0.292346 0.415307 2.07334 1.13681 0.466941 0.0661187 1.13681 1.59567 0.371211 0.257578 1.59567 1.23297 0.445022 0.109957 1.23297 1.08964 0.478086 0.043829 1.08964 3.01006 0.183017 0.633966 3.01006 EXPONENTIAL_CDF_TEST Normal end of execution. EXPONENTIAL_SAMPLE_TEST Python version: 3.6.5 EXPONENTIAL_MEAN computes the Exponential mean EXPONENTIAL_SAMPLE samples the Exponential distribution EXPONENTIAL_VARIANCE computes the Exponential variance. PDF parameter A = 1 PDF parameter B = 10 PDF mean = 11 PDF variance = 100 Sample size = 1000 Sample mean = 11.0328 Sample variance = 98.1133 Sample maximum = 62.6979 Sample minimum = 1.0184 EXPONENTIAL_SAMPLE_TEST Normal end of execution. EXPONENTIAL_01_CDF_TEST Python version: 3.6.5 EXPONENTIAL_01_CDF evaluates the Exponential 01 CDF. EXPONENTIAL_01_CDF_INV inverts the Exponential 01 CDF. EXPONENTIAL_01_PDF evaluates the Exponential 01 PDF. X PDF CDF CDF_INV 0.246436 0.781582 0.218418 0.246436 3.13081 0.0436824 0.956318 3.13081 1.76907 0.170491 0.829509 1.76907 0.824841 0.438305 0.561695 0.824841 0.536668 0.584693 0.415307 0.536668 0.068406 0.933881 0.0661187 0.068406 0.297837 0.742422 0.257578 0.297837 0.116485 0.890043 0.109957 0.116485 0.0448185 0.956171 0.043829 0.0448185 1.00503 0.366034 0.633966 1.00503 EXPONENTIAL_01_SAMPLE_TEST Normal end of execution. EXPONENTIAL_01_SAMPLE_TEST Python version: 3.6.5 EXPONENTIAL_01_MEAN computes the Exponential 01 mean EXPONENTIAL_01_SAMPLE samples the Exponential 01 distribution EXPONENTIAL_01_VARIANCE computes the Exponential 01 variance. PDF mean = 1 PDF variance = 1 Sample size = 1000 Sample mean = 1.00328 Sample variance = 0.981133 Sample maximum = 6.16979 Sample minimum = 0.00184006 EXPONENTIAL_01_SAMPLE_TEST Normal end of execution. EXTREME_VALUES_CDF_TEST Python version: 3.6.5 EXTREME_VALUES_CDF evaluates the Extreme Values CDF EXTREME_VALUES_CDF_INV inverts the Extreme Values CDF. EXTREME_VALUES_PDF evaluates the Extreme Values PDF PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 0.741219 0.110763 0.218418 0.741219 11.3257 0.014238 0.956318 11.3257 7.03121 0.0516842 0.829509 7.03121 3.6508 0.107994 0.561695 3.6508 2.38781 0.121649 0.415307 2.38781 -0.997815 0.0598662 0.0661187 -0.997815 1.08542 0.116462 0.257578 1.08542 -0.37581 0.080916 0.109957 -0.37581 -1.42066 0.0456911 0.043829 -1.42066 4.35736 0.0963122 0.633966 4.35736 EXTREME_VALUES_CDF_TEST Normal end of execution. EXTREME_VALUES_SAMPLE_TEST Python version: 3.6.5 EXTREME_VALUES_MEAN computes the Extreme Values mean EXTREME_VALUES_SAMPLE samples the Extreme Values distribution EXTREME_VALUES_VARIANCE computes the Extreme Values variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 3.73165 PDF variance = 14.8044 Sample size = 1000 Sample mean = 3.74498 Sample variance = 14.6723 Sample maximum = 20.5062 Sample minimum = -3.52111 EXTREME_VALUES_SAMPLE_TEST Normal end of execution. F_CDF_TEST Python version: 3.6.5 F_CDF evaluates the F CDF. F_PDF evaluates the F PDF. PDF parameter M = 1 PDF parameter N = 1 X M N PDF CDF 8.79828 1 1 0.0109522 0.207007 0.913042 1 1 0.174133 0.514474 0.552007 1 1 0.276048 0.593208 0.00347467 1 1 5.38129 0.962517 0.0161641 1 1 2.46383 0.919493 0.0212137 1 1 2.14006 0.907924 1.26646 1 1 0.124798 0.462491 0.00713115 1 1 3.74269 0.946367 2.23222 1 1 0.0659146 0.375501 0.060063 1 1 1.22522 0.846995 F_CDF_TEST Normal end of execution. F_SAMPLE_TEST Python version: 3.6.5 F_MEAN computes the F mean F_SAMPLE samples the F distribution F_VARIANCE computes the F variance. PDF parameter M = 8 PDF parameter N = 6 PDF mean = 1.5 PDF variance = 3.375 Sample size = 1000 Sample mean = 1.65874 Sample variance = 29.2135 Sample maximum = 164.816 Sample minimum = 0.0826478 F_SAMPLE_TEST Normal end of execution. FERMI_DIRAC_SAMPLE_TEST Python version: 3.6.5 FERMI_DIRAC_SAMPLE samples the Fermi Dirac distribution. U = 1 V = 1 SAMPLE_NUM = 10000 Sample mean = 0.595778 Sample variance = 0.175762 Maximum value = 2.59989 Minimum value = 9.85564e-05 U = 2 V = 1 SAMPLE_NUM = 10000 Sample mean = 1.04686 Sample variance = 0.43191 Maximum value = 3.51644 Minimum value = 0.000187922 U = 4 V = 1 SAMPLE_NUM = 10000 Sample mean = 2.01803 Sample variance = 1.43756 Maximum value = 5.40369 Minimum value = 0.000375606 U = 8 V = 1 SAMPLE_NUM = 10000 Sample mean = 3.99861 Sample variance = 5.45539 Maximum value = 9.26709 Minimum value = 0.000751212 U = 16 V = 1 SAMPLE_NUM = 10000 Sample mean = 7.97895 Sample variance = 21.5306 Maximum value = 17.1139 Minimum value = 0.00150242 U = 32 V = 1 SAMPLE_NUM = 10000 Sample mean = 15.949 Sample variance = 85.8381 Maximum value = 32.9504 Minimum value = 0.00300485 U = 1 V = 0.25 SAMPLE_NUM = 10000 Sample mean = 0.504508 Sample variance = 0.0898473 Maximum value = 1.35092 Minimum value = 9.39015e-05 FERMI_DIRAC_SAMPLE_TEST Normal end of execution. FISHER_PDF_TEST Python version: 3.6.5 FISHER_PDF evaluates the Fisher PDF. PDF parameters: Concentration parameter KAPPA = 0 1 0 0 X PDF -0.563163 -0.223966 -0.795416 0.0795775 0.659018 -0.28431 0.696321 0.0795775 -0.169386 0.397757 -0.901719 0.0795775 -0.484844 0.557308 -0.674043 0.0795775 -0.912342 -0.305351 0.27275 0.0795775 -0.876546 0.150061 0.457329 0.0795775 -0.197387 -0.979903 -0.0287825 0.0795775 0.594574 0.00928713 -0.803987 0.0795775 0.795008 0.489058 0.358866 0.0795775 -0.81091 0.0500046 -0.58303 0.0795775 PDF parameters: Concentration parameter KAPPA = 0.5 1 0 0 X PDF -0.36265 -0.252581 -0.897044 0.0636934 0.771936 -0.2403 0.588533 0.112322 0.0772099 0.402384 -0.912209 0.0793613 -0.267118 0.614061 -0.742682 0.0668096 -0.854781 -0.387061 0.345736 0.0498 -0.798383 0.187733 0.572137 0.0512243 0.0489331 -0.998371 -0.029325 0.0782472 0.725749 0.00794632 -0.687913 0.109758 0.866032 0.403105 0.295795 0.117733 -0.698933 0.061115 -0.712572 0.0538359 PDF parameters: Concentration parameter KAPPA = 10 1 0 0 X PDF 0.847866 -0.143704 -0.510366 0.347624 0.981308 -0.0727455 0.178165 1.3202 0.912126 0.165435 -0.375043 0.660982 0.864357 0.320442 -0.387562 0.409948 0.687254 -0.54176 0.483919 0.069756 0.721497 0.215876 0.657906 0.0982419 0.908697 -0.417276 -0.0122566 0.638699 0.977346 0.00244466 -0.211634 1.26892 0.989186 0.118246 0.0867674 1.42842 0.764132 0.0551224 -0.642701 0.150473 FISHER_PDF_TEST Normal end of execution. FISK_CDF_TEST Python version: 3.6.5 FISK_CDF evaluates the Fisk CDF FISK_CDF_INV inverts the Fisk CDF. FISK_PDF evaluates the Fisk PDF PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 2.30758 0.391667 0.218418 2.30758 6.59494 0.0223993 0.956318 6.59494 4.38899 0.125191 0.829509 4.38899 3.17239 0.339985 0.561695 3.17239 2.78448 0.408233 0.415307 2.78448 1.82738 0.223887 0.0661187 1.82738 2.40534 0.408224 0.257578 2.40534 1.99609 0.29475 0.109957 1.99609 1.71577 0.175649 0.043829 1.71577 3.40184 0.289844 0.633966 3.40184 FISK_CDF_TEST Normal end of execution. FISK_SAMPLE_TEST Python version: 3.6.5 FISK_MEAN computes the Fisk mean FISK_SAMPLE samples the Fisk distribution FISK_VARIANCE computes the Fisk variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 3.4184 PDF variance = 3.82494 Sample size = 1000 Sample mean = 3.4112 Sample variance = 2.91484 Sample maximum = 16.6277 Sample minimum = 1.24516 FISK_SAMPLE_TEST Normal end of execution. FOLDED_NORMAL_CDF_TEST Python version: 3.6.5 FOLDED_NORMAL_CDF evaluates the Folded Normal CDF. FOLDED_NORMAL_CDF_INV inverts the Folded Normal CDF. FOLDED_NORMAL_PDF evaluates the Folded Normal PDF. PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 1.03703 0.205965 0.218421 1.03703 7.16445 0.0314698 0.956292 7.16364 4.97681 0.0901798 0.829447 4.97609 2.86891 0.163148 0.561656 2.86863 2.03443 0.186808 0.415234 2.03394 0.310759 0.212331 0.0661153 0.310758 1.22833 0.203183 0.257565 1.22824 0.517615 0.211208 0.109931 0.517593 0.206128 0.212686 0.043879 0.206146 3.33313 0.147866 0.633889 3.33255 FOLDED_NORMAL_CDF_TEST Normal end of execution. FOLDED_NORMAL_SAMPLE_TEST Python version: 3.6.5 FOLDED_NORMAL_MEAN computes the Folded Normal mean FOLDED_NORMAL_SAMPLE samples the Folded Normal distribution FOLDED_NORMAL_VARIANCE computes the Folded Normal variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2.90672 PDF variance = 4.55099 Sample size = 1000 Sample mean = 2.92096 Sample variance = 4.50179 Sample maximum = 10.6319 Sample minimum = 0.00881944 FOLDED_NORMAL_SAMPLE_TEST Normal end of execution. FRECHET_CDF_TEST Python version: 3.6.5 FRECHET_CDF evaluates the Frechet CDF FRECHET_CDF_INV inverts the Frechet CDF. FRECHET_PDF evaluates the Frechet PDF PDF parameter ALPHA = 3 X PDF CDF CDF_INV 2.92711 0.0392689 0.960911 2.92711 0.663048 0.502421 0.0323688 0.663048 0.640129 0.394778 0.0220955 0.640129 0.991316 1.11292 0.358255 0.991316 0.848505 1.12612 0.194572 0.848505 0.820631 1.08312 0.163737 0.820631 2.41384 0.0823022 0.931368 2.41384 1.12607 0.926203 0.496424 1.12607 1.03496 1.0609 0.405736 1.03496 0.861648 1.14004 0.209468 0.861648 FRECHET_CDF_TEST Normal end of execution. FRECHET_SAMPLE_TEST Python version: 3.6.5 FRECHET_MEAN computes the Frechet mean FRECHET_SAMPLE samples the Frechet distribution FRECHET_VARIANCE computes the Frechet variance. PDF parameter ALPHA = 3 PDF mean = 1.35412 PDF variance = 0.845303 Sample size = 1000 Sample mean = 1.35005 Sample variance = 0.61922 Sample maximum = 7.81659 Sample minimum = 0.541476 FRECHET_SAMPLE_TEST Normal end of execution. GAMMA_CDF_TEST Python version: 3.6.5 GAMMA_CDF evaluates the Gamma CDF. GAMMA_PDF evaluates the Gamma PDF. PDF parameter A = 1 PDF parameter B = 1.5 PDF parameter C = 3 X PDF CDF 9.78938 0.0326457 0.931465 3.52763 0.175509 0.238845 4.49151 0.176127 0.411287 7.07259 0.0953344 0.768902 5.28905 0.156175 0.544577 14.503 0.0033268 0.993778 8.13457 0.0648279 0.853273 10.4424 0.024378 0.94997 5.8157 0.138588 0.622277 4.28548 0.178916 0.37469 GAMMA_CDF_TEST Normal end of execution. GAMMA_SAMPLE_TEST Python version: 3.6.5 GAMMA_MEAN computes the Gamma mean GAMMA_SAMPLE samples the Gamma distribution GAMMA_VARIANCE computes the Gamma variance. TEST NUMBER: 0 PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 2 PDF mean = 7 PDF variance = 18 Sample size = 1000 Sample mean = 7.13589 Sample variance = 18.7835 Sample maximum = 32.6521 Sample minimum = 1.12016 TEST NUMBER: 1 PDF parameter A = 2 PDF parameter B = 0.5 PDF parameter C = 0.5 PDF mean = 2.25 PDF variance = 0.125 Sample size = 1000 Sample mean = 2.25244 Sample variance = 0.106096 Sample maximum = 4.46484 Sample minimum = 2 GAMMA_SAMPLE_TEST Normal end of execution. GAMMA_INC_VALUES_TEST: Python version: 3.6.5 GAMMA_INC_VALUES stores values of the incomplete Gamma function. A X GAMMA_INC(A,X) 0.100000 0.030000 2.49030283630057 0.100000 0.300000 0.8718369702247978 0.100000 1.500000 0.1079213896175866 0.500000 0.075000 1.238121685818417 0.500000 0.750000 0.3911298052193973 0.500000 3.500000 0.01444722098952533 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.006737946999085467 1.100000 0.100000 0.8827966752611692 1.100000 1.000000 0.3908330082003269 1.100000 5.000000 0.008051456628620992 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.00729505572443613 6.000000 2.500000 114.9574754165633 6.000000 12.000000 2.440923530031405 11.000000 16.000000 280854.6620274718 26.000000 25.000000 8.576480283455533e+24 41.000000 45.000000 2.085031346403364e+47 GAMMA_INC_VALUES_TEST: Normal end of execution. GAMMA_VALUES_TEST: Python version: 3.6.5 GAMMA_VALUES stores values of the Gamma function. X GAMMA(X) -0.500000 -3.5449077018110322 -0.010000 -100.5871979644108052 0.010000 99.4325851191506018 0.100000 9.5135076986687324 0.200000 4.5908437119988026 0.400000 2.2181595437576882 0.500000 1.7724538509055161 0.600000 1.4891922488128171 0.800000 1.1642297137253030 1.000000 1.0000000000000000 1.100000 0.9513507698668732 1.200000 0.9181687423997607 1.300000 0.8974706963062772 1.400000 0.8872638175030753 1.500000 0.8862269254527581 1.600000 0.8935153492876903 1.700000 0.9086387328532904 1.800000 0.9313837709802427 1.900000 0.9617658319073874 2.000000 1.0000000000000000 3.000000 2.0000000000000000 4.000000 6.0000000000000000 10.000000 362880.0000000000000000 20.000000 121645100408832000.0000000000000000 30.000000 8841761993739701898620088352768.0000000000000000 GAMMA_VALUES_TEST: Normal end of execution. GEOMETRIC_CDF_TEST Python version: 3.6.5 GEOMETRIC_CDF evaluates the Geometric CDF GEOMETRIC_CDF_INV inverts the Geometric CDF. GEOMETRIC_PDF evaluates the Geometric PDF PDF parameter A = 0.25 X PDF CDF CDF_INV 1 0.25 0.25 2 11 0.0140784 0.957765 12 7 0.0444946 0.866516 8 3 0.140625 0.578125 4 2 0.1875 0.4375 3 1 0.25 0.25 2 2 0.1875 0.4375 3 1 0.25 0.25 2 1 0.25 0.25 2 4 0.105469 0.683594 5 GEOMETRIC_CDF_TEST Normal end of execution. GEOMETRIC_SAMPLE_TEST Python version: 3.6.5 GEOMETRIC_MEAN computes the Geometric mean GEOMETRIC_SAMPLE samples the Geometric distribution GEOMETRIC_VARIANCE computes the Geometric variance. PDF parameter A = 0.25 PDF mean = 4 PDF variance = 12 Sample size = 1000 Sample mean = 4.022 Sample variance = 11.7413 Sample maximum = 22 Sample minimum = 1 GEOMETRIC_SAMPLE_TEST Normal end of execution. GOMPERTZ_CDF_TEST Python version: 3.6.5 GOMPERTZ_CDF evaluates the Gompertz CDF GOMPERTZ_CDF_INV inverts the Gompertz CDF. GOMPERTZ_PDF evaluates the Gompertz PDF PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 0.0798917 2.47825 0.218418 0.0798917 0.785233 0.225843 0.956318 0.785233 0.494408 0.720533 0.829509 0.494408 0.251663 1.56551 0.561695 0.251663 0.168638 1.97158 0.415307 0.168638 0.0226237 2.84592 0.0661187 0.0226237 0.0960122 2.38054 0.257578 0.0960122 0.0383151 2.74199 0.109957 0.0383151 0.0148627 2.89822 0.043829 0.0148627 0.301249 1.35309 0.633966 0.301249 GOMPERTZ_CDF_TEST Normal end of execution. GOMPERTZ_SAMPLE_TEST Python version: 3.6.5 GOMPERTZ_SAMPLE samples the Gompertz distribution PDF parameter A = 2 PDF parameter B = 3 Sample size = 1000 Sample mean = 0.279586 Sample variance = 0.0569063 Sample maximum = 1.2783 Sample minimum = 0.000613224 GOMPERTZ_SAMPLE_TEST Normal end of execution. GUMBEL_CDF_TEST Python version: 3.6.5 GUMBEL_CDF evaluates the Gumbel CDF. GUMBEL_CDF_INV inverts the Gumbel CDF. GUMBEL_PDF evaluates the Gumbel PDF. X PDF CDF CDF_INV -0.419594 0.332289 0.218418 -0.419594 3.10856 0.0427141 0.956318 3.10856 1.67707 0.155053 0.829509 1.67707 0.550268 0.323983 0.561695 0.550268 0.12927 0.364946 0.415307 0.12927 -0.999272 0.179599 0.0661187 -0.999272 -0.304859 0.349387 0.257578 -0.304859 -0.791937 0.242748 0.109957 -0.791937 -1.14022 0.137073 0.043829 -1.14022 0.785788 0.288936 0.633966 0.785788 GUMBEL_CDF_TEST Normal end of execution. GUMBEL_SAMPLE_TEST Python version: 3.6.5 GUMBEL_MEAN computes the Gumbel mean GUMBEL_SAMPLE samples the Gumbel distribution GUMBEL_VARIANCE computes the Gumbel variance. PDF mean = 0.577216 PDF variance = 1.64493 Sample size = 1000 Sample mean = 0.581659 Sample variance = 1.63026 Sample maximum = 6.16874 Sample minimum = -1.84037 GUMBEL_SAMPLE_TEST Normal end of execution. HALF_NORMAL_CDF_TEST Python version: 3.6.5 HALF_NORMAL_CDF evaluates the Half Normal CDF. HALF_NORMAL_CDF_INV inverts the Half Normal CDF. HALF_NORMAL_PDF evaluates the Half Normal PDF. PDF parameter A = 0 PDF parameter B = 2 X PDF CDF CDF_INV 0.554517 0.383899 0.218418 0.554517 4.03425 0.0521654 0.956318 4.03425 2.74126 0.155945 0.829509 2.74126 1.55012 0.295438 0.561695 1.55012 1.09309 0.343595 0.415307 1.09309 0.165925 0.397572 0.0661187 0.165925 0.657295 0.377969 0.257578 0.657295 0.276499 0.395148 0.109957 0.276499 0.109918 0.39834 0.043829 0.109918 1.80785 0.265145 0.633966 1.80785 HALF_NORMAL_CDF_TEST Normal end of execution. HALF_NORMAL_SAMPLE_TEST Python version: 3.6.5 HALF_NORMAL_MEAN computes the Half Normal mean HALF_NORMAL_SAMPLE samples the Half Normal distribution HALF_NORMAL_VARIANCE computes the Half Normal variance. PDF parameter A = 0 PDF parameter B = 10 PDF mean = 7.97885 PDF variance = 36.338 Sample size = 1000 Sample mean = 8.01612 Sample variance = 35.9155 Sample maximum = 30.769 Sample minimum = 0.0230406 HALF_NORMAL_SAMPLE_TEST Normal end of execution. HYPERGEOMETRIC_CDF_TEST Python version: 3.6.5 HYPERGEOMETRIC_CDF evaluates the Hypergeometric CDF. HYPERGEOMETRIC_PDF evaluates the Hypergeometric PDF. PDF argument X = 7 Total number of balls = 100 Number of white balls = 7 Number of balls taken = 10 PDF value = = 7.49646e-09 CDF value = = 1 HYPERGEOMETRIC_CDF_TEST Normal end of execution. HYPERGEOMETRIC_SAMPLE_TEST Python version: 3.6.5 HYPERGEOMETRIC_MEAN computes the Hypergeometric mean HYPERGEOMETRIC_SAMPLE samples the Hypergeometric distribution HYPERGEOMETRIC_VARIANCE computes the Hypergeometric variance. PDF parameter N = 10 PDF parameter M = 7 PDF parameter L = 100 PDF mean = 0.7 PDF variance = 0.591818 Sample size = 1000 Sample mean = 0.709 Sample variance = 0.576896 Sample maximum = 3 Sample minimum = 0 HYPERGEOMETRIC_SAMPLE_TEST Normal end of execution. I4_CHOOSE_TEST Python version: 3.6.5 I4_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 I4_CHOOSE_TEST: Normal end of execution. I4_CHOOSE_LOG_TEST Python version: 3.6.5 I4_CHOOSE_LOG evaluates log(C(N,K)). N K lcnk elcnk CNK 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 2 0 0 1 1 2 1 0.693147 2 2 2 2 0 1 1 3 0 0 1 1 3 1 1.09861 3 3 3 2 1.09861 3 3 3 3 0 1 1 4 0 0 1 1 4 1 1.38629 4 4 4 2 1.79176 6 6 4 3 1.38629 4 4 4 4 0 1 1 I4_CHOOSE_LOG_TEST Normal end of execution. I4_IS_POWER_OF_10_TEST Python version: 3.6.5 I4_IS_POWER_OF_10 reports whether an I4 is a power of 10. I I4_IS_POWER_OF_10(I) 97 False 98 False 99 False 100 True 101 False 102 False 103 False I4_IS_POWER_OF_10_TEST: Normal end of execution. I4_UNIFORM_AB_TEST Python version: 3.6.5 I4_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 1 -35 2 187 3 149 4 69 5 25 6 -81 7 -23 8 -67 9 -87 10 90 11 -82 12 35 13 20 14 127 15 139 16 -100 17 170 18 5 19 -72 20 -96 I4_UNIFORM_AB_TEST: Normal end of execution. I4MAT_PRINT_TEST: Python version: 3.6.5 Test I4MAT_PRINT, which prints an I4MAT. A 5 x 6 integer matrix: Col: 0 1 2 3 4 Row 0: 11 12 13 14 15 1: 21 22 23 24 25 2: 31 32 33 34 35 3: 41 42 43 44 45 4: 51 52 53 54 55 Col: 5 Row 0: 16 1: 26 2: 36 3: 46 4: 56 I4MAT_PRINT_TEST: Normal end of execution. I4MAT_PRINT_SOME_TEST Python version: 3.6.5 I4MAT_PRINT_SOME prints some of an I4MAT. Here is I4MAT, rows 0:2, cols 3:5: Col: 3 4 5 Row 0: 14 15 16 1: 24 25 26 2: 34 35 36 I4MAT_PRINT_SOME_TEST: Normal end of execution. I4ROW_MAX_TEST Python version: 3.6.5 I4ROW_MAX computes maximums of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 Row maximums: 0 4 1 8 2 12 I4ROW_MAX_TEST: Normal end of execution. I4ROW_MEAN_TEST Python version: 3.6.5 I4ROW_MEAN computes row means of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 The row means: 0: 2.5 1: 6.5 2: 10.5 I4ROW_MEAN_TEST: Normal end of execution. I4ROW_MIN_TEST Python version: 3.6.5 I4ROW_MIN computes minimums of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 Row minimums: 0 1 1 5 2 9 I4ROW_MIN_TEST: Normal end of execution. I4ROW_VARIANCE_TEST Python version: 3.6.5 I4ROW_VARIANCE computes variances of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 The row variances: 0: 1.66667 1: 1.66667 2: 1.66667 I4ROW_VARIANCE_TEST: Normal end of execution. I4VEC_MAX_TEST Python version: 3.6.5 I4VEC_MAX returns the maximum entry in an I4VEC. The vector: 0 7 1 29 2 25 3 17 4 13 5 2 6 8 7 4 8 2 9 20 Maximum entry = 29 I4VEC_MAX_TEST Normal end of execution. I4VEC_MEAN_TEST Python version: 3.6.5 I4VEC_MEAN computes the mean of an I4VEC. The vector: 0 2 1 10 2 9 3 6 4 4 The mean value is 6.2 I4VEC_MEAN_TEST: Normal end of execution. I4VEC_MIN_TEST Python version: 3.6.5 I4VEC_MIN returns the minimum entry in an I4VEC. The vector: 0 7 1 29 2 25 3 17 4 13 5 2 6 8 7 4 8 2 9 20 Minimum entry = 2 I4VEC_MIN_TEST Normal end of execution. I4VEC_PRINT_TEST Python version: 3.6.5 I4VEC_PRINT prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 I4VEC_PRINT_TEST: Normal end of execution. I4VEC_RUN_COUNT_TEST Python version: 3.6.5 I4VEC_RUN_COUNT counts runs in an I4VEC Run Count Sequence 9 0 1 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 0 12 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 1 0 1 0 0 14 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 8 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 10 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 1 1 0 1 0 11 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1 0 1 1 1 11 1 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 0 1 15 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 0 1 1 0 12 1 1 0 1 1 1 0 1 0 1 1 0 0 0 1 0 1 1 1 0 14 1 1 0 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 1 0 I4VEC_RUN_COUNT_TEST: Normal end of execution. I4VEC_SUM_TEST Python version: 3.6.5 I4VEC_SUM sums the entries of an I4VEC. The vector: 0 2 1 10 2 9 3 6 4 4 The vector entries sum to 31 I4VEC_SUM_TEST: Normal end of execution. I4VEC_UNIFORM_AB_TEST Python version: 3.6.5 I4VEC_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 The random vector: 0 -35 1 187 2 149 3 69 4 25 5 -81 6 -23 7 -67 8 -87 9 90 10 -82 11 35 12 20 13 127 14 139 15 -100 16 170 17 5 18 -72 19 -96 I4VEC_UNIFORM_AB_TEST: Normal end of execution. I4VEC_UNIQUE_COUNT_TEST Python version: 3.6.5 I4VEC_UNIQUE_COUNT counts unique entries in an I4VEC. Input vector: 0 4 1 20 2 17 3 11 4 8 5 1 6 5 7 2 8 0 9 13 10 1 11 9 12 8 13 15 14 16 15 0 16 18 17 7 18 1 19 0 Number of unique entries is 15 I4VEC_UNIQUE_COUNT_TEST: Normal end of execution. I4VEC_VARIANCE_TEST Python version: 3.6.5 I4VEC_VARIANCE computes the variance of an I4VEC. Input vector: 0 -3 1 5 2 4 3 1 4 -1 5 -5 6 -3 7 -4 8 -5 9 1 Value = 13.1111 I4VEC_VARIANCE_TEST: Normal end of execution. INVERSE_GAUSSIAN_CDF_TEST Python version: 3.6.5 INVERSE_GAUSSIAN_CDF evaluates the Inverse Gaussian CDF. INVERSE_GAUSSIAN_PDF evaluates the Inverse Gaussian PDF. PDF parameter A = 5 PDF parameter B = 2 X PDF CDF 0.559532 0.329239 0.0861168 1.28731 0.251704 0.307572 0.853592 0.319635 0.18353 1.35825 0.241176 0.325052 5.32365 0.0458954 0.744699 0.226285 0.0933236 0.00436661 0.366732 0.244354 0.0287975 2.59887 0.123228 0.539812 0.741461 0.332202 0.146927 1.89165 0.176781 0.435385 INVERSE_GAUSSIAN_CDF_TEST Normal end of execution. INVERSE_GAUSSIAN_SAMPLE_TEST Python version: 3.6.5 INVERSE_GAUSSIAN_MEAN computes the Inverse Gaussian mean INVERSE_GAUSSIAN_SAMPLE samples the Inverse Gaussian distribution INVERSE_GAUSSIAN_VARIANCE computes the Inverse Gaussian variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 2.66667 Sample size = 1000 Sample mean = 1.95731 Sample variance = 2.26428 Sample maximum = 12.1368 Sample minimum = 0.215551 INVERSE_GAUSSIAN_SAMPLE_TEST Normal end of execution. LAPLACE_CDF_TEST Python version: 3.6.5 LAPLACE_CDF evaluates the Laplace CDF LAPLACE_CDF_INV inverts the Laplace CDF. LAPLACE_PDF evaluates the Laplace PDF PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV -0.656392 0.109209 0.218418 -0.656392 5.87532 0.0218412 0.956318 5.87532 3.15185 0.0852454 0.829509 3.15185 1.26339 0.219152 0.561695 1.26339 0.62882 0.207654 0.415307 0.62882 -3.04631 0.0330594 0.0661187 -3.04631 -0.326573 0.128789 0.257578 -0.326573 -2.02904 0.0549784 0.109957 -2.02904 -3.86862 0.0219145 0.043829 -3.86862 1.62376 0.183017 0.633966 1.62376 LAPLACE_CDF_TEST Normal end of execution. LAPLACE_SAMPLE_TEST Python version: 3.6.5 LAPLACE_MEAN computes the Laplace mean LAPLACE_SAMPLE samples the Laplace distribution LAPLACE_VARIANCE computes the Laplace variance. PDF parameter A = 1 PDF parameter B = 2 PDF mean = 1 PDF variance = 8 Sample size = 1000 Sample mean = 0.994018 Sample variance = 8.10829 Sample maximum = 11.9533 Sample minimum = -10.2115 LAPLACE_SAMPLE_TEST Normal end of execution. LEVY_CDF_TEST Python version: 3.6.5 LEVY_CDF evaluates the Levy CDF LEVY_CDF_INV inverts the Levy CDF. LEVY_PDF evaluates the Levy PDF PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV 2.32036 0.174367 0.218418 2.32036 667.596 3.27326e-05 0.956318 667.596 44.1337 0.00194595 0.829509 44.1337 6.93865 0.032943 0.561695 6.93865 4.01406 0.0773762 0.415307 4.01406 1.59227 0.228757 0.0661187 1.59227 2.56039 0.152493 0.257578 2.56039 1.78283 0.227065 0.109957 1.78283 1.49223 0.214227 0.043829 1.49223 9.82141 0.0192259 0.633966 9.82141 LEVY_CDF_TEST Normal end of execution. LOG_NORMAL_CDF_TEST Python version: 3.6.5 LOG_NORMAL_CDF evaluates the Log Normal CDF LOG_NORMAL_CDF_INV inverts the Log Normal CDF. LOG_NORMAL_PDF evaluates the Log Normal PDF PDF parameter A = 10 PDF parameter B = 2.25 X PDF CDF CDF_INV 3829.62 3.42207e-05 0.218418 3829.62 1.03126e+06 3.98836e-08 0.956318 1.03126e+06 187683 6.00352e-07 0.829509 187683 31236.9 5.60821e-06 0.561695 31236.9 13611.8 1.27314e-05 0.415307 13611.8 744.708 7.66792e-05 0.0661187 744.708 5093.04 2.8169e-05 0.257578 5093.04 1393.81 5.99421e-05 0.109957 1393.81 472.134 8.73521e-05 0.043829 472.134 47588.4 3.51376e-06 0.633966 47588.4 LOG_NORMAL_CDF_TEST Normal end of execution. LOG_NORMAL_SAMPLE_TEST Python version: 3.6.5 LOG_NORMAL_MEAN computes the Log Normal mean LOG_NORMAL_SAMPLE samples the Log Normal distribution LOG_NORMAL_VARIANCE computes the Log Normal variance. PDF parameter A = 1 PDF parameter B = 2 PDF mean = 20.0855 PDF variance = 21623 Sample size = 1000 Sample mean = 18.2209 Sample variance = 3776.12 Sample maximum = 835.466 Sample minimum = 0.00815371 LOG_NORMAL_SAMPLE_TEST Normal end of execution. LOG_SERIES_CDF_TEST Python version: 3.6.5 LOG_SERIES_CDF evaluates the Log Series CDF LOG_SERIES_CDF_INV inverts the Log Series CDF. LOG_SERIES_PDF evaluates the Log Series PDF PDF parameter A = 0.25 X PDF CDF CDF_INV 1 0.869015 0.869015 2 1 0.869015 0.869015 2 2 0.108627 0.977642 3 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 4 0.00339459 0.999141 5 1 0.869015 0.869015 2 2 0.108627 0.977642 3 LOG_SERIES_CDF_TEST Normal end of execution. LOG_SERIES_SAMPLE_TEST Python version: 3.6.5 LOG_SERIES_MEAN computes the Log Series mean LOG_SERIES_VARIANCE computes the Log Series variance LOG_SERIES_SAMPLE samples the Log Series distribution. PDF parameter A = 0.25 PDF mean = 1.15869 PDF variance = 0.202361 Sample size = 1000 Sample mean = 1.165 Sample variance = 0.213989 Sample maximum = 4 Sample minimum = 1 LOG_SERIES_SAMPLE_TEST Normal end of execution. LOG_UNIFORM_CDF_TEST Python version: 3.6.5 LOG_UNIFORM_CDF evaluates the Log Uniform CDF LOG_UNIFORM_CDF_INV inverts the Log Uniform CDF. LOG_UNIFORM_PDF evaluates the Log Uniform PDF PDF parameter A = 2 PDF parameter B = 20 X PDF CDF CDF_INV 3.30711 0.131322 0.218418 3.30711 18.0862 0.0240125 0.956318 18.0862 13.5064 0.0321547 0.829509 13.5064 7.28996 0.0595743 0.561695 7.28996 5.204 0.083454 0.415307 5.204 2.32889 0.186481 0.0661187 2.32889 3.61916 0.119999 0.257578 3.61916 2.57624 0.168577 0.109957 2.57624 2.21238 0.196302 0.043829 2.21238 8.60985 0.0504416 0.633966 8.60985 LOG_UNIFORM_CDF_TEST Normal end of execution. LOG_UNIFORM_SAMPLE_TEST Python version: 3.6.5 LOG_UNIFORM_MEAN computes the Log Uniform mean LOG_UNIFORM_SAMPLE samples the Log Uniform distribution LOG_UNIFORM_VARIANCE computes the Log Uniform variance PDF parameter A = 2 PDF parameter B = 20 PDF mean = 7.8173 PDF variance = 24.8801 Sample size = 1000 Sample mean = 7.8421 Sample variance = 24.5202 Sample maximum = 19.9039 Sample minimum = 2.00848 LOG_UNIFORM_SAMPLE_TEST Normal end of execution. LOGISTIC_CDF_TEST Python version: 3.6.5 LOGISTIC_CDF evaluates the Logistic CDF LOGISTIC_CDF_INV inverts the Logistic CDF. LOGISTIC_PDF evaluates the Logistic PDF PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV -1.54982 0.0853559 0.218418 -1.54982 7.17229 0.0208871 0.956318 7.17229 4.16431 0.0707118 0.829509 4.16431 1.49609 0.123097 0.561695 1.49609 0.315863 0.121414 0.415307 0.315863 -4.29579 0.0308735 0.0661187 -4.29579 -1.11719 0.0956157 0.257578 -1.11719 -3.18237 0.0489331 0.109957 -3.18237 -5.16528 0.020954 0.043829 -5.16528 2.09854 0.116027 0.633966 2.09854 LOGISTIC_CDF_TEST Normal end of execution. LOGISTIC_SAMPLE_TEST Python version: 3.6.5 LOGISTIC_MEAN computes the Logistic mean LOGISTIC_SAMPLE samples the Logistic distribution LOGISTIC_VARIANCE computes the Logistic variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 29.6088 Sample size = 1000 Sample mean = 2.00703 Sample variance = 29.8759 Sample maximum = 20.5031 Sample minimum = -16.8911 LOGISTIC_SAMPLE_TEST Normal end of execution. LORENTZ_CDF_TEST Python version: 3.6.5 LORENTZ_CDF evaluates the Lorentz CDF LORENTZ_CDF_INV inverts the Lorentz CDF. LORENTZ_PDF evaluates the Lorentz PDF X PDF CDF CDF_INV -1.2211 0.12778 0.218418 -1.2211 7.24111 0.00595711 0.956318 7.24111 1.68497 0.0829119 0.829509 1.68497 0.196286 0.306501 0.561695 0.196286 -0.272532 0.296302 0.415307 -0.272532 -4.74478 0.0135377 0.0661187 -4.74478 -0.953486 0.16673 0.257578 -0.953486 -2.77879 0.0364964 0.109957 -2.77879 -7.21659 0.0059969 0.043829 -7.21659 0.447611 0.26518 0.633966 0.447611 LORENTZ_CDF_TEST Normal end of execution. LORENTZ_SAMPLE_TEST Python version: 3.6.5 LORENTZ_MEAN computes the Lorentz mean LORENTZ_VARIANCE computes the Lorentz variance LORENTZ_SAMPLE samples the Lorentz distribution. PDF mean = 0 PDF variance = 1e+30 Sample size = 1000 Sample mean = -0.111859 Sample variance = 175.49 Sample maximum = 152.177 Sample minimum = -173.146 LORENTZ_SAMPLE_TEST Normal end of execution. MAXWELL_CDF_TEST Python version: 3.6.5 MAXWELL_CDF evaluates the Maxwell CDF. MAXWELL_CDF_INV inverts the Maxwell CDF. MAXWELL_PDF evaluates the Maxwell PDF. PDF parameter A = 2 X PDF CDF CDF_INV 4.29456 0.183427 0.768636 4.29492 6.13704 0.0338961 0.89487 6.13672 1.45642 0.162283 0.307636 1.45605 5.98388 0.040642 0.887603 5.98438 3.74497 0.242317 0.709648 3.74414 2.0281 0.245322 0.433405 2.02832 1.7946 0.214758 0.383889 1.79492 1.95034 0.235816 0.417222 1.9502 1.49461 0.168514 0.316485 1.49463 1.35125 0.144944 0.282999 1.35156 MAXWELL_CDF_TEST Normal end of execution. MAXWELL_SAMPLE_TEST Python version: 3.6.5 MAXWELL_MEAN computes the Maxwell mean MAXWELL_VARIANCE computes the Maxwell variance MAXWELL_SAMPLE samples the Maxwell distribution. PDF parameter A = 2 PDF mean = 3.19154 PDF mean = 1.81408 Sample size = 1000 Sample mean = 3.15337 Sample variance = 1.9332 Sample maximum = 8.32689 Sample minimum = 0.206015 MAXWELL_SAMPLE_TEST Normal end of execution. MULTINOMIAL_COEF_TEST Python version: 3.6.5 MULTINOMIAL_COEF1 computes multinomial coefficients using the Gamma function MULTINOMIAL_COEF2 computes multinomial coefficients directly. Line 10 of the BINOMIAL table: 0 10 1 1 1 9 10 10 2 8 45 45 3 7 120 120 4 6 210 210 5 5 252 252 6 4 210 210 7 3 120 120 8 2 45 45 9 1 10 10 10 0 1 1 Level 5 of the TRINOMIAL coefficients: 0 0 5 1 1 0 1 4 5 5 0 2 3 10 10 0 3 2 10 10 0 4 1 5 5 0 5 0 1 1 1 0 4 5 5 1 1 3 20 20 1 2 2 30 30 1 3 1 20 20 1 4 0 5 5 2 0 3 10 10 2 1 2 30 30 2 2 1 30 30 2 3 0 10 10 3 0 2 10 10 3 1 1 20 20 3 2 0 10 10 4 0 1 5 5 4 1 0 5 5 5 0 0 1 1 MULTINOMIAL_COEF_TEST Normal end of execution. MULTINOMIAL_PDF_TEST Python version: 3.6.5 MULTINOMIAL_PDF evaluates the Multinomial PDF. PDF argument X: 0 0 1 2 2 3 PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 0: 0.1 1: 0.5 2: 0.4 PDF value = 0.16 MULTINOMIAL_PDF_TEST Normal end of execution. MULTINOMIAL_SAMPLE_TEST Python version: 3.6.5 MULTINOMIAL_MEAN computes the Multinomial mean MULTINOMIAL_SAMPLE samples the Multinomial distribution MULTINOMIAL_VARIANCE computes the Multinomial variance PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 0: 0.125 1: 0.5 2: 0.375 PDF means and variances: 0.625 0.546875 2.5 1.25 1.875 1.17188 Sample size = 1000 Component Min, Max, Mean, Variance: 0 0 3 0.628 0.552169 1 0 5 2.472 1.23446 2 0 5 1.9 1.20721 MULTINOMIAL_SAMPLE_TEST Normal end of execution. NAKAGAMI_CDF_TEST Python version: 3.6.5 NAKAGAMI_CDF evaluates the Nakagami CDF NAKAGAMI_PDF evaluates the Nakagami PDF X PDF CDF CDF_INV 3.18257 0.586699 0.692394 3.18258 3.2582 0.540746 0.735053 3.2582 3.31623 0.503068 0.765346 3.31623 3.36515 0.470346 0.789159 3.36515 3.40825 0.441184 0.808803 3.40825 3.44721 0.414809 0.82548 3.44721 3.48305 0.390724 0.839911 3.48305 3.5164 0.36858 0.852572 3.5164 3.54772 0.348118 0.863796 3.54772 3.57735 0.329135 0.873828 3.57735 NAKAGAMI_CDF_TEST Normal end of execution. NAKAGAMI_SAMPLE_TEST Python version: 3.6.5 NAKAGAMI_MEAN computes the Nakagami mean NAKAGAMI_VARIANCE computes the Nakagami variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 2.91874 PDF variance = 0.318446 NAKAGAMI_SAMPLE_TEST Normal end of execution. NEGATIVE_BINOMIAL_CDF_TEST Python version: 3.6.5 NEGATIVE_BINOMIAL_CDF evaluates the Negative Binomial CDF. NEGATIVE_BINOMIAL_CDF_INV inverts the Negative Binomial CDF. NEGATIVE_BINOMIAL_PDF evaluates the Negative Binomial PDF. PDF parameter A = 2 PDF parameter B = 0.25 X PDF CDF CDF_INV 6 0.098877 0.466064 6 3 0.09375 0.15625 3 7 0.0889893 0.555054 7 4 0.105469 0.261719 4 4 0.105469 0.261719 4 13 0.0316764 0.873295 13 8 0.0778656 0.632919 8 6 0.098877 0.466064 6 12 0.0387155 0.841618 12 6 0.098877 0.466064 6 NEGATIVE_BINOMIAL_CDF_TEST Normal end of execution. NEGATIVE_BINOMIAL_SAMPLE_TEST Python version: 3.6.5 NEGATIVE_BINOMIAL_MEAN computes the Negative Binomial mean NEGATIVE_BINOMIAL_SAMPLE samples the Negative Binomial distribution NEGATIVE_BINOMIAL_VARIANCE computes the Negative Binomial variance. PDF parameter A = 2 PDF parameter B = 0.75 PDF mean = 2.66667 PDF variance = 0.888889 Sample size = 1000 Sample mean = 2.688 Sample variance = 0.833489 Sample maximum = 8 Sample minimum = 2 NEGATIVE_BINOMIAL_SAMPLE_TEST Normal end of execution. NORMAL_01_CDF_TEST Python version: 3.6.5 NORMAL_01_CDF evaluates the Normal 01 CDF NORMAL_01_CDF_INV inverts the Normal 01 CDF. NORMAL_01_PDF evaluates the Normal 01 PDF X PDF CDF CDF_INV 1.67904 0.0974392 0.953428 1.67904 -0.56606 0.339884 0.285677 -0.56606 1.21293 0.191179 0.887423 1.21293 1.26938 0.178244 0.897847 1.26938 -1.66609 0.0995733 0.0478481 -1.66609 -2.24246 0.0322815 0.0124657 -2.24246 0.0396749 0.398628 0.515824 0.0396749 0.673068 0.318081 0.749548 0.673068 -0.275127 0.384125 0.391609 -0.275127 2.164 0.0383732 0.984768 2.164 NORMAL_01_CDF_TEST Normal end of execution. NORMAL_01_CDF_VALUES_TEST: Python version: 3.6.5 NORMAL_01_CDF_VALUES stores values of the unit normal CDF. X NORMAL_01_CDF(X) 0.000000 0.5000000000000000 0.100000 0.5398278372770290 0.200000 0.5792597094391030 0.300000 0.6179114221889526 0.400000 0.6554217416103242 0.500000 0.6914624612740131 0.600000 0.7257468822499270 0.700000 0.7580363477769270 0.800000 0.7881446014166033 0.900000 0.8159398746532405 1.000000 0.8413447460685429 1.500000 0.9331927987311419 2.000000 0.9772498680518208 2.500000 0.9937903346742240 3.000000 0.9986501019683699 3.500000 0.9997673709209645 4.000000 0.9999683287581669 NORMAL_01_CDF_VALUES_TEST: Normal end of execution. NORMAL_01_SAMPLE_TEST Python version: 3.6.5 NORMAL_01_MEAN computes the Normal 01 mean NORMAL_01_SAMPLE samples the Normal 01 distribution NORMAL_01_VARIANCE returns the Normal 01 variance. PDF mean = 0 PDF variance = 1 Sample size = 1000 Sample mean = 0.00581875 Sample variance = 0.998375 Sample maximum = 3.32858 Sample minimum = -3.02975 NORMAL_01_SAMPLE_TEST Normal end of execution. NORMAL_CDF_TEST Python version: 3.6.5 NORMAL_CDF evaluates the Normal CDF NORMAL_CDF_INV inverts the Normal CDF. NORMAL_PDF evaluates the Normal PDF PDF parameter A = 100 PDF parameter B = 15 X PDF CDF CDF_INV 125.186 0.00649595 0.953428 125.186 91.5091 0.0226589 0.285677 91.5091 118.194 0.0127453 0.887423 118.194 119.041 0.0118829 0.897847 119.041 75.0087 0.00663822 0.0478481 75.0087 66.363 0.0021521 0.0124657 66.363 100.595 0.0265752 0.515824 100.595 110.096 0.0212054 0.749548 110.096 95.8731 0.0256084 0.391609 95.8731 132.46 0.00255821 0.984768 132.46 NORMAL_CDF_TEST Normal end of execution. NORMAL_SAMPLE_TEST Python version: 3.6.5 NORMAL_MEAN computes the Normal mean NORMAL_SAMPLE samples the Normal distribution NORMAL_VARIANCE returns the Normal variance. PDF parameter A = 100 PDF parameter B = 15 PDF mean = 100 PDF variance = 225 Sample size = 1000 Sample mean = 100.087 Sample variance = 224.634 Sample maximum = 149.929 Sample minimum = 54.5537 NORMAL_SAMPLE_TEST Normal end of execution. NORMAL_TRUNCATED_AB_CDF_TEST Python version: 3.6.5 NORMAL_TRUNCATED_AB_CDF evaluates the Normal Truncated AB CDF. NORMAL_TRUNCATED_AB_CDF_INV inverts the Normal Truncated AB CDF. NORMAL_TRUNCATED_AB_PDF evaluates the Normal Truncated AB PDF. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] X PDF CDF CDF_INV 81.63 0.0127629 0.218418 81.63 137.962 0.00527826 0.956318 137.962 122.367 0.0112043 0.829509 122.367 103.704 0.0165359 0.561695 103.704 94.899 0.016374 0.415307 94.899 65.8326 0.00657044 0.0661187 65.8326 84.5743 0.0138204 0.257578 84.5743 71.5672 0.00875626 0.109957 71.5672 62.0654 0.00528716 0.043829 62.0654 108.155 0.0158521 0.633966 108.155 NORMAL_TRUNCATED_AB_CDF_TEST Normal end of execution. NORMAL_TRUNCATED_AB_SAMPLE_TEST Python version: 3.6.5 NORMAL_TRUNCATED_AB_MEAN computes the Normal Truncated AB mean NORMAL_TRUNCATED_AB_SAMPLE samples the Normal Truncated AB distribution NORMAL_TRUNCATED_AB_VARIANCE computes the Normal Truncated AB variance. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] PDF mean = 100 PDF variance = 483.588 Sample size = 1000 Sample mean = 100.123 Sample variance = 486.064 Sample maximum = 149.108 Sample minimum = 50.7873 NORMAL_TRUNCATED_AB_SAMPLE_TEST Normal end of execution. NORMAL_TRUNCATED_A_CDF_TEST Python version: 3.6.5 NORMAL_TRUNCATED_A_CDF evaluates the Normal Truncated A CDF. NORMAL_TRUNCATED_A_CDF_INV inverts the Normal Truncated A CDF. NORMAL_TRUNCATED_A_PDF evaluates the Normal Truncated A PDF. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo) X PDF CDF CDF_INV 82.0355 0.0126136 0.218418 82.0355 143.008 0.00371817 0.956318 143.008 124.191 0.0102245 0.829509 124.191 104.515 0.016065 0.561695 104.515 95.5021 0.016067 0.415307 95.5021 66.0709 0.00650134 0.0661187 66.0709 85.0161 0.0136446 0.257578 85.0161 71.8645 0.00866826 0.109957 71.8645 62.2618 0.00522585 0.043829 62.2618 109.115 0.0152792 0.633966 109.115 NORMAL_TRUNCATED_A_CDF_TEST Normal end of execution. NORMAL_TRUNCATED_A_SAMPLE_TEST Python version: 3.6.5 NORMAL_TRUNCATED_A_MEAN computes the Normal Truncated A mean NORMAL_TRUNCATED_A_SAMPLE samples the Normal Truncated A distribution NORMAL_TRUNCATED_A_VARIANCE computes the Normal Truncated A variance. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo] PDF mean = 101.381 PDF variance = 554.032 Sample size = 1000 Sample mean = 101.504 Sample variance = 555.665 Sample maximum = 171.782 Sample minimum = 50.8055 NORMAL_TRUNCATED_A_SAMPLE_TEST Normal end of execution. NORMAL_TRUNCATED_B_CDF_TEST Python version: 3.6.5 NORMAL_TRUNCATED_B_CDF evaluates the Normal Truncated B CDF. NORMAL_TRUNCATED_B_CDF_INV inverts the Normal Truncated B CDF. NORMAL_TRUNCATED_B_PDF evaluates the Normal Truncated B PDF. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [-oo,150] X PDF CDF CDF_INV 80.1372 0.0119094 0.218418 80.1372 137.766 0.00521699 0.956318 137.766 122.006 0.0110844 0.829509 122.006 103.073 0.0162063 0.561695 103.073 94.0447 0.0158724 0.415307 94.0447 62.0713 0.00516592 0.0661187 62.0713 83.2727 0.0130542 0.257578 83.2727 68.9956 0.00756806 0.109957 68.9956 57.0318 0.00372825 0.043829 57.0318 107.607 0.0155905 0.633966 107.607 NORMAL_TRUNCATED_B_CDF_TEST Normal end of execution. NORMAL_TRUNCATED_B_SAMPLE_TEST Python version: 3.6.5 NORMAL_TRUNCATED_B_MEAN computes the Normal Truncated B mean NORMAL_TRUNCATED_B_SAMPLE samples the Normal Truncated B distribution NORMAL_TRUNCATED_B_VARIANCE computes the Normal Truncated B variance. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [-oo,150] PDF mean = 98.6188 PDF variance = 554.032 Sample size = 1000 Sample mean = 98.7101 Sample variance = 560.281 Sample maximum = 149.087 Sample minimum = 27.2041 NORMAL_TRUNCATED_B_SAMPLE_TEST Normal end of execution. OWEN_VALUES_TEST: Python version: 3.6.5 OWEN_VALUES stores values of the OWEN function. H A T 0.062500 0.250000 0.038912 6.500000 0.437500 0.000000 7.000000 0.968750 0.000000 4.781250 0.062500 0.000000 2.000000 0.500000 0.008625 1.000000 0.999997 0.066742 1.000000 0.500000 0.043065 1.000000 1.000000 0.066742 1.000000 2.000000 0.078468 1.000000 3.000000 0.079300 0.500000 0.500000 0.064489 0.500000 1.000000 0.106671 0.500000 2.000000 0.141581 0.500000 3.000000 0.151084 0.250000 0.500000 0.071347 0.250000 1.000000 0.120129 0.250000 2.000000 0.166613 0.250000 3.000000 0.184750 0.125000 0.500000 0.073173 0.125000 1.000000 0.123763 0.125000 2.000000 0.173744 0.125000 3.000000 0.195119 0.007812 0.500000 0.073789 0.007812 1.000000 0.124995 0.007812 2.000000 0.176198 0.007812 3.000000 0.198777 0.007812 10.000000 0.234089 0.007812 100.000000 0.247946 OWEN_VALUES_TEST: Normal end of execution. PARETO_CDF_TEST Python version: 3.6.5 PARETO_CDF evaluates the Pareto CDF PARETO_CDF_INV inverts the Pareto CDF. PARETO_PDF evaluates the Pareto PDF PDF parameter A = 0.5 PDF parameter B = 5 X PDF CDF CDF_INV 0.525261 7.43994 0.218418 0.525261 0.935209 0.233544 0.956318 0.935209 0.712246 1.19685 0.829509 0.712246 0.589678 3.71647 0.561695 0.589678 0.556653 5.25186 0.415307 0.556653 0.506888 9.21192 0.0661187 0.506888 0.530689 6.99489 0.257578 0.530689 0.511785 8.69547 0.109957 0.511785 0.504502 9.47638 0.043829 0.504502 0.611316 2.99382 0.633966 0.611316 PARETO_CDF_TEST Normal end of execution. PARETO_SAMPLE_TEST Python version: 3.6.5 PARETO_MEAN computes the Pareto mean PARETO_SAMPLE samples the Pareto distribution PARETO_VARIANCE computes the Pareto variance. PDF parameter A = 0.5 PDF parameter B = 5 PDF mean = 0.625 PDF variance = 0.0260417 Sample size = 1000 Sample mean = 0.624896 Sample variance = 0.0234138 Sample maximum = 1.7174 Sample minimum = 0.500184 PARETO_SAMPLE_TEST Normal end of execution. PEARSON_05_PDF_TEST Python version: 3.6.5 PEARSON_05_PDF evaluates the Pearson 05 PDF. PDF argument X = 5 PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF value = 0.0758163 PEARSON_05_PDF_TEST Normal end of execution. PLANCK_PDF_TEST Python version: 3.6.5 PLANCK_PDF evaluates the Planck PDF. PDF parameter A = 2 PDF parameter B = 3 X PDF 3.673 0.0788188 3.0685 0.154193 2.78714 0.203171 5.41214 0.00777678 3.91626 0.0587186 0.782927 0.312254 1.68781 0.41945 2.8936 0.183616 1.24248 0.429598 1.20762 0.42572 PLANCK_PDF_TEST Normal end of execution. PLANCK_SAMPLE_TEST Python version: 3.6.5 PLANCK_MEAN returns the mean of the Planck distribution. PLANCK_SAMPLE samples the Planck distribution. PLANCK_VARIANCE returns the variance of the Planck distribution. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 3.83223 PDF variance = 4.11319 Sample size = 1000 Sample mean = 1.93308 Sample variance = 0.99989 Sample maximum = 6.48678 Sample minimum = 0.165955 PLANCK_SAMPLE_TEST Normal end of execution. POISSON_CDF_TEST Python version: 3.6.5 POISSON_CDF evaluates the Poisson CDF, POISSON_CDF_INV inverts the Poisson CDF. POISSON_PDF evaluates the Poisson PDF. PDF parameter A = 10 X PDF CDF CDF_INV 7 0.0900792 0.220221 7 16 0.0216988 0.972958 16 13 0.0729079 0.864464 13 10 0.12511 0.58304 10 9 0.12511 0.45793 9 5 0.0378333 0.067086 5 8 0.112599 0.33282 8 6 0.0630555 0.130141 6 5 0.0378333 0.067086 5 11 0.113736 0.696776 11 POISSON_CDF_TEST Normal end of execution. POISSON_SAMPLE_TEST Python version: 3.6.5 POISSON_MEAN computes the Poisson mean POISSON_SAMPLE samples the Poisson distribution POISSON_VARIANCE computes the Poisson variance. PDF parameter A = 10 PDF mean = 10 PDF variance = 10 Sample size = 1000 Sample mean = 10.005 Sample variance = 10.005 Sample maximum = 20 Sample minimum = 2 POISSON_SAMPLE_TEST Normal end of execution. POWER_CDF_TEST Python version: 3.6.5 POWER_CDF evaluates the Power CDF POWER_CDF_INV inverts the Power CDF. POWER_PDF evaluates the Power PDF PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 1.40206 0.311568 0.218418 1.40206 2.93374 0.651943 0.956318 2.93374 2.73232 0.607183 0.829509 2.73232 2.24839 0.499642 0.561695 2.24839 1.93333 0.429629 0.415307 1.93333 0.771407 0.171424 0.0661187 0.771407 1.52256 0.338347 0.257578 1.52256 0.994792 0.221065 0.109957 0.994792 0.628061 0.139569 0.043829 0.628061 2.38866 0.530813 0.633966 2.38866 POWER_CDF_TEST Normal end of execution. POWER_SAMPLE_TEST Python version: 3.6.5 POWER_MEAN computes the Power mean POWER_SAMPLE samples the Power distribution POWER_VARIANCE computes the Power variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 0.5 Sample size = 1000 Sample mean = 2.00568 Sample variance = 0.505123 Sample maximum = 2.99686 Sample minimum = 0.128629 POWER_SAMPLE_TEST Normal end of execution. PSI_VALUES_TEST: Python version: 3.6.5 PSI_VALUES stores values of the PSI function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 PSI_VALUES_TEST: Normal end of execution. QUASIGEOMETRIC_CDF_TEST Python version: 3.6.5 QUASIGEOMETRIC_CDF evaluates the Quasigeometric CDF QUASIGEOMETRIC_CDF_INV inverts the Quasigeometric CDF. QUASIGEOMETRIC_PDF evaluates the Quasigeometric PDF PDF parameter A = 0.4825 PDF parameter B = 0.5893 X PDF CDF CDF_INV 0 0.4825 0.4825 1 5 0.0256319 0.963222 6 3 0.0738088 0.894094 4 1 0.212537 0.695037 2 0 0.4825 0.4825 1 0 0.4825 0.4825 1 0 0.4825 0.4825 1 0 0.4825 0.4825 1 0 0.4825 0.4825 1 1 0.212537 0.695037 2 QUASIGEOMETRIC_CDF_TEST Normal end of execution. QUASIGEOMETRIC_SAMPLE_TEST QUASIGEOMETRIC_MEAN computes the Quasigeometric mean QUASIGEOMETRIC_SAMPLE samples the Quasigeometric distribution QUASIGEOMETRIC_VARIANCE computes the Quasigeometric variance. PDF parameter A = 0.4825 PDF parameter B = 0.5893 PDF parameter A = 0.4825 PDF mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.267 Sample variance = 3.21693 Sample maximum = 11 Sample minimum = 0 QUASIGEOMETRIC_SAMPLE_TEST Normal end of execution. R8_BETA_TEST: Python version: 3.6.5 R8_BETA evaluates the BETA function. X Y BETA(X,Y) R8_BETA(X,Y) tabulated computed. 0.2 1 5 4.999999999999999 0.4 1 2.5 2.5 0.6 1 1.666666666666667 1.666666666666667 0.8 1 1.25 1.25 1 0.2 5 4.999999999999999 1 0.4 2.5 2.5 1 1 1 1 2 2 0.1666666666666667 0.1666666666666667 3 3 0.03333333333333333 0.03333333333333333 4 4 0.007142857142857143 0.007142857142857143 5 5 0.001587301587301587 0.001587301587301587 6 2 0.02380952380952381 0.02380952380952381 6 3 0.005952380952380952 0.005952380952380952 6 4 0.001984126984126984 0.001984126984126984 6 5 0.0007936507936507937 0.0007936507936507937 6 6 0.0003607503607503608 0.0003607503607503605 7 7 8.325008325008325e-05 8.32500832500834e-05 R8_BETA_TEST: Normal end of execution. R8_CSC_TEST Python version: 3.6.5 R8_CSC computes the cosecant of an angle. ANGLE R8_CSC(ANGLE) 0.00 Undefined 15.00 1.46037 30.00 -1.00194 45.00 1.29876 60.00 -8.05172 75.00 -1.69796 90.00 1.0177 105.00 -1.18588 120.00 4.05727 135.00 2.06607 150.00 -1.05049 165.00 1.10683 180.00 Undefined 195.00 -2.69119 210.00 1.10311 225.00 -1.05294 240.00 2.09321 255.00 3.94632 270.00 -1.18053 285.00 1.0191 300.00 -1.71484 315.00 -7.61642 330.00 1.29113 345.00 -1.00241 360.00 Undefined R8_CSC_TEST Normal end of execution. R8_EPSILON_TEST Python version: 3.6.5 R8_EPSILON produces the R8 roundoff unit. R = R8_EPSILON() = 2.220446e-16 ( 1 + R ) - 1 = 2.220446e-16 ( 1 + (R/2) ) - 1 = 0.000000e+00 R8_EPSILON_TEST Normal end of execution. R8_ERF_TEST: Python version: 3.6.5 R8_ERF evaluates the error function. X ERF(X) R8_ERF(X) 0 0 0 0.1 0.1124629160182849 0.1124629160182849 0.2 0.2227025892104785 0.2227025892104785 0.3 0.3286267594591274 0.3286267594591273 0.4 0.4283923550466685 0.4283923550466684 0.5 0.5204998778130465 0.5204998778130465 0.6 0.6038560908479259 0.6038560908479259 0.7 0.6778011938374185 0.6778011938374184 0.8 0.7421009647076605 0.7421009647076605 0.9 0.7969082124228321 0.7969082124228322 1 0.8427007929497149 0.8427007929497148 1.1 0.8802050695740817 0.8802050695740817 1.2 0.9103139782296354 0.9103139782296354 1.3 0.9340079449406524 0.9340079449406524 1.4 0.9522851197626488 0.9522851197626487 1.5 0.9661051464753106 0.9661051464753108 1.6 0.976348383344644 0.976348383344644 1.7 0.9837904585907746 0.9837904585907746 1.8 0.9890905016357306 0.9890905016357308 1.9 0.9927904292352575 0.9927904292352574 2 0.9953222650189527 0.9953222650189527 R8_ERF_TEST Normal end of execution. R8_FACTORIAL_TEST Python version: 3.6.5 R8_FACTORIAL evaluates the factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 6 6 4 24 24 5 120 120 6 720 720 7 5040 5040 8 40320 40320 9 362880 362880 10 3628800 3628800 11 39916800 39916800 12 479001600 479001600 13 6227020800 6227020800 14 87178291200 87178291200 15 1307674368000 1307674368000 16 20922789888000 20922789888000 17 355687428096000 355687428096000 18 6402373705728000 6402373705728000 19 1.21645100408832e+17 1.21645100408832e+17 20 2.43290200817664e+18 2.43290200817664e+18 25 1.551121004333099e+25 1.551121004333099e+25 50 3.041409320171338e+64 3.041409320171338e+64 100 9.332621544394415e+157 9.33262154439441e+157 150 5.713383956445855e+262 5.71338395644585e+262 R8_FACTORIAL_TEST Normal end of execution. R8_FACTORIAL_VALUES_TEST: Python version: 3.6.5 R8_FACTORIAL_VALUES returns values of the real factorial function. N R8_FACTORIAL(N) 0 1 1 1 2 2 3 6 4 24 5 120 6 720 7 5040 8 40320 9 362880 10 3.6288e+06 11 3.99168e+07 12 4.79002e+08 13 6.22702e+09 14 8.71783e+10 15 1.30767e+12 16 2.09228e+13 17 3.55687e+14 18 6.40237e+15 19 1.21645e+17 20 2.4329e+18 25 1.55112e+25 50 3.04141e+64 100 9.33262e+157 150 5.71338e+262 R8_FACTORIAL_VALUES_TEST: Normal end of execution. R8_GAMMA_TEST: Python version: 3.6.5 R8_GAMMA evaluates the Gamma function. X GAMMA(X) R8_GAMMA(X) -0.5 -3.544907701811032 -3.544907701811032 -0.01 -100.5871979644108 -100.5871979644108 0.01 99.4325851191506 99.4325851191506 0.1 9.513507698668732 9.513507698668731 0.2 4.590843711998803 4.590843711998803 0.4 2.218159543757688 2.218159543757688 0.5 1.772453850905516 1.772453850905516 0.6 1.489192248812817 1.489192248812817 0.8 1.164229713725303 1.164229713725303 1 1 1 1.1 0.9513507698668732 0.9513507698668732 1.2 0.9181687423997607 0.9181687423997607 1.3 0.8974706963062772 0.8974706963062772 1.4 0.8872638175030753 0.8872638175030754 1.5 0.8862269254527581 0.8862269254527581 1.6 0.8935153492876903 0.8935153492876903 1.7 0.9086387328532904 0.9086387328532904 1.8 0.9313837709802427 0.9313837709802427 1.9 0.9617658319073874 0.9617658319073874 2 1 1 3 2 2 4 6 6 10 362880 362880 20 1.21645100408832e+17 1.216451004088321e+17 30 8.841761993739702e+30 8.841761993739751e+30 R8_GAMMA_TEST Normal end of execution. R8_GAMMA_INC_TEST: Python version: 3.6.5 R8_GAMMA_INC evaluates the normalized incomplete Gamma function P(A,X). A X Exact F R8_GAMMA_INC(A,X) 0.1 0.03 2.4903 0.738235 0.1 0.3 0.871837 0.908358 0.1 1.5 0.107921 0.988656 0.5 0.075 1.23812 0.301465 0.5 0.75 0.39113 0.779329 0.5 3.5 0.0144472 0.991849 1 0.1 0.904837 0.0951626 1 1 0.367879 0.632121 1 5 0.00673795 0.993262 1.1 0.1 0.882797 0.0720597 1.1 1 0.390833 0.589181 1.1 5 0.00805146 0.991537 2 0.15 0.989814 0.0101858 2 1.5 0.557825 0.442175 2 7 0.00729506 0.992705 6 2.5 114.957 0.042021 6 12 2.44092 0.979659 11 16 280855 0.922604 26 25 8.57648e+24 0.447079 41 45 2.08503e+47 0.744455 R8_GAMMA_INC_TEST Normal end of execution. R8_GAMMA_LOG_TEST: Python version: 3.6.5 R8_GAMMA_LOG evaluates the logarithm of the Gamma function. X GAMMA_LOG(X) R8_GAMMA_LOG(X) 0.2 1.524063822430784 1.524063822430784 0.4 0.7966778177017837 0.7966778177017837 0.6 0.3982338580692348 0.3982338580692349 0.8 0.1520596783998375 0.1520596783998376 1 0 0 1.1 -0.04987244125983972 -0.04987244125983976 1.2 -0.08537409000331583 -0.08537409000331585 1.3 -0.1081748095078604 -0.1081748095078605 1.4 -0.1196129141723712 -0.1196129141723713 1.5 -0.1207822376352452 -0.1207822376352453 1.6 -0.1125917656967557 -0.1125917656967558 1.7 -0.09580769740706586 -0.09580769740706586 1.8 -0.07108387291437215 -0.07108387291437215 1.9 -0.03898427592308333 -0.03898427592308337 2 0 0 3 0.6931471805599453 0.6931471805599454 4 1.791759469228055 1.791759469228055 10 12.80182748008147 12.80182748008147 20 39.33988418719949 39.33988418719949 30 71.25703896716801 71.257038967168 R8_GAMMA_LOG_TEST Normal end of execution. R8_GAMMA_LOG_INT_TEST Python version: 3.6.5 R8_GAMMA_LOG_INT evaluates the logarithm of the gamma function for integer argument. I R8_GAMMA_LOG_INT(I) 1 0 2 0 3 0.693147 4 1.79176 5 3.17805 6 4.78749 7 6.57925 8 8.52516 9 10.6046 10 12.8018 11 15.1044 12 17.5023 13 19.9872 14 22.5522 15 25.1912 16 27.8993 17 30.6719 18 33.5051 19 36.3954 20 39.3399 R8_GAMMA_LOG_TEST Normal end of execution. R8_HUGE_TEST Python version: 3.6.5 R8_HUGE returns a "huge" R8; R8_HUGE = 1.79769e+308 R8_HUGE_TEST Normal end of execution. R8_UNIFORM_01_TEST Python version: 3.6.5 R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 R8_UNIFORM_01_TEST Normal end of execution. R8_ZETA_TEST Python version: 3.6.5 R8_ZETA estimates the Zeta function. P R8_Zeta(P) 1 1.79769e+308 2 1.64493 3 1.20206 4 1.08232 5 1.03693 6 1.01734 7 1.00835 8 1.00408 9 1.00201 10 1.00099 11 1.00049 12 1.00025 13 1.00012 14 1.00006 15 1.00003 16 1.00002 17 1.00001 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 3 1.20206 3.125 1.17905 3.25 1.15915 3.375 1.14185 3.5 1.12673 3.625 1.11347 3.75 1.10179 3.875 1.09147 4 1.08232 R8_ZETA_TEST Normal end of execution. R8MAT_PRINT_TEST Python version: 3.6.5 R8MAT_PRINT prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 R8MAT_PRINT_TEST: Normal end of execution. R8MAT_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_PRINT_SOME prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8MAT_PRINT_SOME_TEST: Normal end of execution. R8POLY_PRINT_TEST Python version: 3.6.5 R8POLY_PRINT prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 R8POLY_PRINT_TEST: Normal end of execution. R8POLY_VALUE_HORNER_TEST Python version: 3.6.5 R8POLY_VALUE_HORNER evaluates a polynomial at a point using Horners method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X P(X) 0 0.0000 24 1 0.3333 10.8642 2 0.6667 3.45679 3 1.0000 0 4 1.3333 -0.987654 5 1.6667 -0.691358 6 2.0000 0 7 2.3333 0.493827 8 2.6667 0.493827 9 3.0000 0 10 3.3333 -0.691358 11 3.6667 -0.987654 12 4.0000 0 13 4.3333 3.45679 14 4.6667 10.8642 15 5.0000 24 R8POLY_VALUE_HORNER_TEST: Normal end of execution. R8ROW_MAX_TEST Python version: 3.6.5 R8ROW_MAX computes maximums of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 Row maximums: 0: 4 1: 8 2: 12 R8ROW_MAX_TEST: Normal end of execution. R8ROW_MEAN_TEST Python version: 3.6.5 R8ROW_MEAN computes row means of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 The row means: 0: 2.5 1: 6.5 2: 10.5 R8ROW_MEAN_TEST: Normal end of execution. R8ROW_MIN_TEST Python version: 3.6.5 R8ROW_MIN computes minimums of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 Row minimums: 0: 1 1: 5 2: 9 R8ROW_MIN_TEST: Normal end of execution. R8ROW_VARIANCE_TEST Python version: 3.6.5 R8ROW_VARIANCE computes variances of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 The row variances: 0: 1.66667 1: 1.66667 2: 1.66667 R8ROW_VARIANCE_TEST: Normal end of execution. R8VEC_DOT_PRODUCT_TEST: Python version: 3.6.5 R8VEC_DOT_PRODUCT computes the dot product of two R8VEC's. V1 and V2: 0: 0.218418 0.0617272 1: 0.956318 0.449539 2: 0.829509 0.401306 3: 0.561695 0.754673 4: 0.415307 0.797287 5: 0.0661187 0.00183837 6: 0.257578 0.897504 7: 0.109957 0.350752 8: 0.043829 0.0945448 9: 0.633966 0.0136169 V1 dot V2 = 1.81393 R8VEC_DOT_PRODUCT_TEST: Normal end of execution. R8VEC_MAX_TEST Python version: 3.6.5 R8VEC_MAX computes the maximum entry in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Max = 9.12635 R8VEC_MAX_TEST: Normal end of execution. R8VEC_MEAN_TEST Python version: 3.6.5 R8VEC_MEAN computes the mean of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Value = -0.907304 R8VEC_MEAN_TEST: Normal end of execution. R8VEC_MIN_TEST Python version: 3.6.5 R8VEC_MIN computes the minimum entry in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Min = -9.12342 R8VEC_MIN_TEST: Normal end of execution. R8VEC_NORM_TEST Python version: 3.6.5 R8VEC_NORM computes the L2 norm of an R8VEC. Input vector: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 L2 norm = 1.62017 R8VEC_NORM_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_SUM_TEST Python version: 3.6.5 R8VEC_SUM sums the entries in an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 Sum of entries = -18.1461 R8VEC_SUM_TEST: Normal end of execution. R8VEC_TRANSPOSE_PRINT_TEST Python version: 3.6.5 R8VEC_TRANSPOSE_PRINT prints an R8VEC "tranposed", that is, placing multiple entries on a line. The vector X: 0.218418 0.956318 0.829509 0.561695 0.415307 0.0661187 0.257578 0.109957 0.043829 0.633966 0.0617272 0.449539 R8VEC_TRANSPOSE_PRINT_TEST Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. R8VEC_UNIFORM_AB_TEST Python version: 3.6.5 R8VEC_UNIFORM_AB computes a random R8VEC. -1 <= X <= 5 Initial seed is 123456789 Random R8VEC: 0: 0.31051 1: 4.73791 2: 3.97706 3: 2.37017 4: 1.49184 5: -0.603288 6: 0.545467 7: -0.340259 8: -0.737026 9: 2.80379 R8VEC_UNIFORM_AB_TEST: Normal end of execution. R8VEC_VARIANCE_TEST Python version: 3.6.5 R8VEC_VARIANCE computes the variance of an R8VEC. Input vector: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 5: -4.33881 6: -2.42422 7: -3.90043 8: -4.56171 9: 1.33966 Value = 10.5549 R8VEC_VARIANCE_TEST: Normal end of execution. R8VEC2_PRINT_TEST Python version: 3.6.5 R8VEC2_PRINT prints a pair of R8VEC's. Print a pair of R8VEC's: 0: 0 0 1: 0.2 0.04 2: 0.4 0.16 3: 0.6 0.36 4: 0.8 0.64 5: 1 1 R8VEC2_PRINT_TEST: Normal end of execution. RAYLEIGH_CDF_TEST Python version: 3.6.5 RAYLEIGH_CDF evaluates the Rayleigh CDF RAYLEIGH_CDF_INV inverts the Rayleigh CDF. RAYLEIGH_PDF evaluates the Rayleigh PDF PDF parameter A = 2 X PDF CDF CDF_INV 1.4041 0.274354 0.218418 1.4041 5.00465 0.0546538 0.956318 5.00465 3.76199 0.160346 0.829509 3.76199 2.5688 0.281479 0.561695 2.5688 2.07204 0.302877 0.415307 2.07204 0.739762 0.172712 0.0661187 0.739762 1.5436 0.286501 0.257578 1.5436 0.96534 0.214799 0.109957 0.96534 0.598789 0.143136 0.043829 0.598789 2.83553 0.259475 0.633966 2.83553 RAYLEIGH_CDF_TEST Normal end of execution. RAYLEIGH_SAMPLE_TEST Python version: 3.6.5 RAYLEIGH_MEAN computes the Rayleigh mean RAYLEIGH_SAMPLE samples the Rayleigh distribution RAYLEIGH_VARIANCE computes the Rayleigh variance. PDF parameter A = 2 PDF mean = 2.50663 PDF variance = 1.71681 Sample size = 1000 Sample mean = 2.5139 Sample variance = 1.70827 Sample maximum = 7.02555 Sample minimum = 0.121328 RAYLEIGH_SAMPLE_TEST Normal end of execution. RECIPROCAL_CDF_TEST Python version: 3.6.5 RECIPROCAL_CDF evaluates the Reciprocal CDF. RECIPROCAL_CDF_INV inverts the Reciprocal CDF. RECIPROCAL_PDF evaluates the Reciprocal PDF. PDF parameter A = 1 PDF parameter B = 3 X PDF CDF CDF_INV 1.27119 0.71605 0.218418 1.27119 2.85943 0.318329 0.956318 2.85943 2.48758 0.365914 0.829509 2.48758 1.85352 0.491087 0.561695 1.85352 1.57816 0.576771 0.415307 1.57816 1.07534 0.846465 0.0661187 1.07534 1.32708 0.685898 0.257578 1.32708 1.1284 0.806664 0.109957 1.1284 1.04933 0.867449 0.043829 1.04933 2.00668 0.453604 0.633966 2.00668 RECIPROCAL_CDF_TEST Normal end of execution. RECIPROCAL_SAMPLE_TEST Python version: 3.6.5 RECIPROCAL_MEAN computes the Reciprocal mean RECIPROCAL_SAMPLE samples the Reciprocal distribution RECIPROCAL_VARIANCE computes the Reciprocal variance. PDF parameter A = 1 PDF parameter B = 3 PDF mean = 1.82048 PDF variance = 0.326815 Sample size = 1000 Sample mean = 1.8251 Sample variance = 0.321955 Sample maximum = 2.99311 Sample minimum = 1.00202 RECIPROCAL_SAMPLE_TEST Normal end of execution. SECH_CDF_TEST Python version: 3.6.5 SECH_CDF evaluates the Sech CDF. SECH_CDF_INV inverts the Sech CDF. SECH_PDF evaluates the Sech PDF. PDF parameter A = 3 PDF parameter B = 2 X PDF CDF CDF_INV 0.941182 0.100839 0.218418 0.941182 8.35531 0.0217727 0.956318 8.35531 5.58635 0.0812276 0.829509 5.58635 3.39009 0.156175 0.561695 3.39009 2.46147 0.153555 0.415307 2.46147 -1.52223 0.0328221 0.0661187 -1.52223 1.3038 0.115187 0.257578 1.3038 -0.492142 0.0538915 0.109957 -0.492142 -2.34859 0.0218453 0.043829 -2.34859 3.86774 0.145266 0.633966 3.86774 SECH_CDF_TEST Normal end of execution. SECH_SAMPLE_TEST Python version: 3.6.5 SECH_MEAN computes the Sech mean SECH_SAMPLE samples the Sech distribution SECH_VARIANCE computes the Sech variance. PDF parameter A = 3 PDF parameter B = 2 PDF mean = 3 PDF variance = 9.8696 Sample size = 1000 Sample mean = 2.99951 Sample variance = 9.97628 Sample maximum = 14.4364 Sample minimum = -8.69458 SECH_SAMPLE_TEST Normal end of execution. SEMICIRCULAR_CDF_TEST Python version: 3.6.5 SEMICIRCULAR_CDF evaluates the Semicircular CDF. SEMICIRCULAR_CDF_INV inverts the Semicircular CDF. SEMICIRCULAR_PDF evaluates the Semicircular PDF. PDF parameter A = 3 PDF parameter B = 2 X PDF CDF CDF_INV 2.07408 0.282143 0.216167 2.07422 2.64915 0.313374 0.388897 2.64941 4.26118 0.247045 0.872972 4.26123 3.95508 0.27967 0.792025 3.95508 2.82894 0.317143 0.445615 2.8291 3.07844 0.318065 0.524963 3.07861 2.09106 0.283538 0.220968 2.09082 4.78579 0.143324 0.979302 4.78516 3.8562 0.287667 0.763967 3.85645 3.6144 0.302918 0.692448 3.61426 SEMICIRCULAR_CDF_TEST Normal end of execution. SEMICIRCULAR_SAMPLE_TEST Python version: 3.6.5 SEMICIRCULAR_MEAN computes the Semicircular mean SEMICIRCULAR_SAMPLE samples the Semicircular distribution SEMICIRCULAR_VARIANCE computes the Semicircular variance. PDF parameter A = 3 PDF parameter B = 2 PDF mean = 3 PDF variance = 1 Sample size = 1000 Sample mean = 3.02688 Sample variance = 0.989554 Sample maximum = 4.96783 Sample minimum = 1.05174 SEMICIRCULAR_SAMPLE_TEST Normal end of execution. SIN_POWER_INT_TEST Python version: 3.6.5 SIN_POWER_INT returns values of the integral of SIN(X)^N from A to B. A B N Exact Computed 10.000000 20.000000 0 1.000000e+01 1.000000e+01 0.000000 1.000000 1 4.596977e-01 4.596977e-01 0.000000 1.000000 2 2.726756e-01 2.726756e-01 0.000000 1.000000 3 1.789406e-01 1.789406e-01 0.000000 1.000000 4 1.240256e-01 1.240256e-01 0.000000 1.000000 5 8.897440e-02 8.897440e-02 0.000000 2.000000 5 9.039312e-01 9.039312e-01 1.000000 2.000000 5 8.149568e-01 8.149568e-01 0.000000 1.000000 10 2.188752e-02 2.188752e-02 0.000000 1.000000 11 1.702344e-02 1.702344e-02 SIN_POWER_INT_TEST Normal end of execution. SIN_POWER_INT_VALUES_TEST: Python version: 3.6.5 SIN_POWER_INT_VALUES stores values of the cosine power integral. A B N F 10.000000 20.000000 0 10 0.000000 1.000000 1 0.4596976941318603 0.000000 1.000000 2 0.2726756432935796 0.000000 1.000000 3 0.1789405625488581 0.000000 1.000000 4 0.1240255653152068 0.000000 1.000000 5 0.08897439645157594 0.000000 2.000000 5 0.9039312384814995 1.000000 2.000000 5 0.8149568420299235 0.000000 1.000000 10 0.02188752242172985 0.000000 1.000000 11 0.01702343937406933 SIN_POWER_INT_VALUES_TEST: Normal end of execution. STIRLING2_TEST: Python version: 3.6.5 STIRLING2 returns Stirling numbers of the second kind. Stirling2 matrix: Col: 0 1 2 3 4 Row 0: 1 0 0 0 0 1: 1 1 0 0 0 2: 1 3 1 0 0 3: 1 7 6 1 0 4: 1 15 25 10 1 5: 1 31 90 65 15 6: 1 63 301 350 140 7: 1 127 966 1701 1050 Col: 5 6 7 Row 0: 0 0 0 1: 0 0 0 2: 0 0 0 3: 0 0 0 4: 0 0 0 5: 1 0 0 6: 21 1 0 7: 266 28 1 STIRLING2_TEST: Normal end of execution. STUDENT_CDF_TEST Python version: 3.6.5 STUDENT_CDF evaluates the Student CDF. STUDENT_PDF evaluates the Student PDF. PDF argument X = 2.447 PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF value = 0.14754 CDF value = 0.816049 STUDENT_CDF_TEST Normal end of execution. STUDENT_SAMPLE_TEST Python version: 3.6.5 STUDENT_MEAN computes the Student mean STUDENT_SAMPLE samples the Student distribution STUDENT_VARIANCE computes the Student variance. PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF mean = 0.5 PDF variance = 6 Sample size = 1000 Sample mean = 0.472733 Sample variance = 3.15695 Sample maximum = 12.2574 Sample minimum = -18.5475 STUDENT_SAMPLE_TEST Normal end of execution. STUDENT_NONCENTRAL_CDF_TEST Python version: 3.6.5 STUDENT_NONCENTRAL_CDF evaluates the Student Noncentral CDF PDF argument X = 0.5 PDF parameter IDF = 10 PDF parameter B = 1 CDF value = 0.30528 STUDENT_NONCENTRAL_CDF_TEST Normal end of execution. TFN_TEST Python version: 3.6.5 TFN evaluates Owen's T function. H A T(H,A) Exact 0.0625 0.25 0.0389119 0.0389119 6.5 0.4375 2.00058e-11 2.00058e-11 7 0.96875 6.39906e-13 6.39906e-13 4.78125 0.0625 1.0633e-07 1.0633e-07 2 0.5 0.00862508 0.00862508 1 0.999997 0.0667418 0.0667418 1 0.5 0.0430647 0.0430647 1 1 0.0667419 0.0667419 1 2 0.0784682 0.0784682 1 3 0.0792995 0.0792995 0.5 0.5 0.0644886 0.0644886 0.5 1 0.106671 0.106671 0.5 2 0.141581 0.141581 0.5 3 0.151084 0.151084 0.25 0.5 0.0713466 0.0713466 0.25 1 0.120129 0.120129 0.25 2 0.166613 0.166613 0.25 3 0.18475 0.18475 0.125 0.5 0.0731727 0.0731727 0.125 1 0.123763 0.123763 0.125 2 0.173744 0.173744 0.125 3 0.195119 0.195119 0.0078125 0.5 0.0737894 0.0737894 0.0078125 1 0.124995 0.124995 0.0078125 2 0.176198 0.176198 0.0078125 3 0.198777 0.198777 0.0078125 10 0.234074 0.234089 0.0078125 100 0.233737 0.247946 TFN_TEST Normal end of execution. TRIANGLE_CDF_TEST Python version: 3.6.5 TRIANGLE_CDF evaluates the Triangle CDF TRIANGLE_CDF_INV inverts the Triangle CDF. TRIANGLE_PDF evaluates the Triangle PDF PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 10 X PDF CDF CDF_INV 2.98281 0.220312 0.218418 2.98281 8.34109 0.0526639 0.956318 8.34109 6.72267 0.104042 0.829509 6.72267 4.74517 0.16682 0.561695 4.74517 3.93076 0.192674 0.415307 3.93076 2.09093 0.121215 0.0661187 2.09093 3.16095 0.217113 0.257578 3.16095 2.40685 0.156316 0.109957 2.40685 1.88821 0.0986903 0.043829 1.88821 5.1979 0.152448 0.633966 5.1979 TRIANGLE_CDF_TEST Normal end of execution. TRIANGLE_SAMPLE_TEST Python version: 3.6.5 TRIANGLE_MEAN returns the Triangle mean TRIANGLE_SAMPLE samples the Triangle distribution TRIANGLE_VARIANCE returns the Triangle variance PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 10 PDF parameter MEAN = 4.66667 PDF parameter VARIANCE = 3.72222 Sample size = 1000 Sample mean = 4.67684 Sample variance = 3.70549 Sample maximum = 9.63699 Sample minimum = 1.18191 TRIANGLE_SAMPLE_TEST Normal end of execution. TRIANGULAR_CDF_TEST Python version: 3.6.5 TRIANGULAR_CDF evaluates the Triangular CDF TRIANGULAR_CDF_INV inverts the Triangular CDF. TRIANGULAR_PDF evaluates the Triangular PDF PDF parameter A = 1 PDF parameter B = 10 X PDF CDF CDF_INV 3.97421 0.146875 0.218418 3.97421 8.66991 0.0656834 0.956318 8.66991 7.37229 0.129764 0.829509 7.37229 5.78677 0.208061 0.561695 5.78677 5.10121 0.202529 0.415307 5.10121 2.6364 0.0808099 0.0661187 2.6364 4.22985 0.159499 0.257578 4.22985 3.11027 0.104211 0.109957 3.11027 2.33232 0.0657935 0.043829 2.33232 6.14975 0.190136 0.633966 6.14975 TRIANGULAR_CDF_TEST Normal end of execution. TRIANGULAR_SAMPLE_TEST Python version: 3.6.5 TRIANGULAR_MEAN computes the Triangular mean TRIANGULAR_SAMPLE samples the Triangular distribution TRIANGULAR_VARIANCE computes the Triangular variance. PDF parameter A = 1 PDF parameter B = 10 PDF mean = 5.5 PDF variance = 3.375 Sample size = 1000 Sample mean = 5.51035 Sample variance = 3.38802 Sample maximum = 9.70895 Sample minimum = 1.27286 TRIANGULAR_SAMPLE_TEST Normal end of execution. TRIGAMMA_TEST: Python version: 3.6.5 TRIGAMMA evaluates the TriGamma function. X FX FX Tabulated Computed 1 1.644934066848226 1.644934065473016 1.1 1.433299150792759 1.43329914968199 1.2 1.267377205423779 1.267377204522996 1.3 1.134253434996619 1.134253434263296 1.4 1.025356590529597 1.025356589930374 1.5 0.9348022005446793 0.9348022000532704 1.6 0.8584318931245799 0.8584318927201864 1.7 0.7932328301639984 0.793232829830095 1.8 0.7369741375017002 0.7369741372251055 1.9 0.6879720582426356 0.6879720580127948 2 0.6449340668482264 0.6449340654730159 TRIGAMMA_TEST Normal end of execution. TRIGAMMA_VALUES_TEST: Python version: 3.6.5 TRIGAMMA_VALUES stores values of the TRIGAMMA function. X TRIGAMMA(X) 1.000000 1.6449340668482260 1.100000 1.4332991507927590 1.200000 1.2673772054237791 1.300000 1.1342534349966189 1.400000 1.0253565905295969 1.500000 0.9348022005446793 1.600000 0.8584318931245799 1.700000 0.7932328301639984 1.800000 0.7369741375017002 1.900000 0.6879720582426356 2.000000 0.6449340668482264 TRIGAMMA_VALUES_TEST: Normal end of execution. UNIFORM_01_CDF_TEST Python version: 3.6.5 UNIFORM_01_CDF evaluates the Uniform 01 CDF UNIFORM_01_CDF_INV inverts the Uniform 01 CDF. UNIFORM_01_PDF evaluates the Uniform 01 PDF X PDF CDF CDF_INV 0.218418 1 0.218418 0.218418 0.956318 1 0.956318 0.956318 0.829509 1 0.829509 0.829509 0.561695 1 0.561695 0.561695 0.415307 1 0.415307 0.415307 0.0661187 1 0.0661187 0.0661187 0.257578 1 0.257578 0.257578 0.109957 1 0.109957 0.109957 0.043829 1 0.043829 0.043829 0.633966 1 0.633966 0.633966 UNIFORM_01_CDF_TEST Normal end of execution. UNIFORM_01_SAMPLE_TEST Python version: 3.6.5 UNIFORM_01_MEAN computes the Uniform 01 mean UNIFORM_01_SAMPLE samples the Uniform 01 distribution UNIFORM_01_VARIANCE computes the Uniform 01 variance. PDF mean = 0.5 PDF variance = 0.0833333 Sample size = 1000 Sample mean = 0.50304 Sample variance = 0.082332 Sample maximum = 0.997908 Sample minimum = 0.00183837 UNIFORM_01_SAMPLE_TEST Normal end of execution. UNIFORM_01_ORDER_SAMPLE_TEST Python version: 3.6.5 UNIFORM_ORDER_SAMPLE samples the Uniform 01 Order distribution. Ordered sample: 0: 0.0174736 1: 0.0275623 2: 0.131654 3: 0.274807 4: 0.385745 5: 0.664103 6: 0.768848 7: 0.834884 8: 0.854621 9: 0.858873 UNIFORM_01_ORDER_SAMPLE_TEST Normal end of execution. UNIFORM_CDF_TEST Python version: 3.6.5 UNIFORM_CDF evaluates the Uniform CDF UNIFORM_CDF_INV inverts the Uniform CDF. UNIFORM_PDF evaluates the Uniform PDF PDF parameter A = 1 PDF parameter B = 10 X PDF CDF CDF_INV 2.96576 0.111111 0.218418 2.96576 9.60686 0.111111 0.956318 9.60686 8.46558 0.111111 0.829509 8.46558 6.05526 0.111111 0.561695 6.05526 4.73776 0.111111 0.415307 4.73776 1.59507 0.111111 0.0661187 1.59507 3.3182 0.111111 0.257578 3.3182 1.98961 0.111111 0.109957 1.98961 1.39446 0.111111 0.043829 1.39446 6.70569 0.111111 0.633966 6.70569 UNIFORM_CDF_TEST Normal end of execution. UNIFORM_SAMPLE_TEST Python version: 3.6.5 UNIFORM_MEAN computes the Uniform mean UNIFORM_SAMPLE samples the Uniform distribution UNIFORM_VARIANCE computes the Uniform variance. PDF parameter A = 1 PDF parameter B = 10 PDF mean = 5.5 PDF variance = 6.75 Sample size = 1000 Sample mean = 5.52736 Sample variance = 6.66889 Sample maximum = 9.98117 Sample minimum = 1.01655 UNIFORM_SAMPLE_TEST Normal end of execution. UNIFORM_DISCRETE_CDF_TEST Python version: 3.6.5 UNIFORM_DISCRETE_CDF evaluates the Uniform Discrete CDF UNIFORM_DISCRETE_CDF_INV inverts the Uniform Discrete CDF. UNIFORM_DISCRETE_PDF evaluates the Uniform Discrete PDF PDF parameter A = 1 PDF parameter B = 6 X PDF CDF CDF_INV 2 0.166667 0.333333 3 6 0.166667 1 6 5 0.166667 0.833333 6 4 0.166667 0.666667 5 3 0.166667 0.5 4 1 0.166667 0.166667 2 2 0.166667 0.333333 3 1 0.166667 0.166667 2 1 0.166667 0.166667 2 4 0.166667 0.666667 5 UNIFORM_DISCRETE_CDF_TEST Normal end of execution. UNIFORM_DISCRETE_SAMPLE_TEST Python version: 3.6.5 UNIFORM_DISCRETE_MEAN computes the Uniform Discrete mean UNIFORM_DISCRETE_SAMPLE samples the Uniform Discrete distribution UNIFORM_DISCRETE_VARIANCE computes the Uniform Discrete variance. PDF parameter A = 1 PDF parameter B = 6 PDF mean = 3.5 PDF variance = 2.91667 Sample size = 1000 Sample mean = 3.527 Sample variance = 2.85012 Sample maximum = 6 Sample minimum = 1 UNIFORM_DISCRETE_SAMPLE_TEST Normal end of execution. UNIFORM_NSPHERE_SAMPLE_TEST Python version: 3.6.5 UNIFORM_NSPHERE_SAMPLE samples the Uniform Nsphere distribution. Dimension N of sphere = 3 Points on the sphere: 0.781938 -0.263617 0.56487 0.413678 -0.542961 -0.730797 0.0544828 0.924277 -0.377813 0.723278 0.0995291 0.683347 0.747038 -0.663815 -0.035826 -0.78339 -0.516512 -0.34571 0.146773 0.598886 -0.78727 -0.649577 -0.399299 -0.647001 0.375237 -0.770087 0.51591 -0.408985 0.0579096 -0.910702 UNIFORM_NSPHERE_SAMPLE_TEST Normal end of execution. VON_MISES_CDF_TEST Python version: 3.6.5 VON_MISES_CDF evaluates the Von Mises CDF. VON_MISES_CDF_INV inverts the Von Mises CDF. VON_MISES_PDF evaluates the Von Mises PDF. PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV 0.476234 0.394559 0.25232 0.476146 1.12227 0.50824 0.562764 1.12233 0.931772 0.51349 0.464857 0.931738 0.575338 0.43192 0.293305 0.575471 0.862805 0.506281 0.429664 0.862709 -1.39044 0.0161849 0.00863675 -1.39301 2.77511 0.0465295 0.974194 2.77328 0.193915 0.278813 0.157223 0.193893 0.786199 0.49292 0.391357 0.78601 0.790531 0.493818 0.393494 0.790612 VON_MISES_CDF_TEST Normal end of execution. VON_MISES_SAMPLE_TEST Python version: 3.6.5 VON_MISES_MEAN computes the Von Mises mean VON_MISES_SAMPLE samples the Von Mises distribution. VON_MISES_CIRCULAR_VARIANCE computes the Von Mises circular variance PDF parameter A = 1 PDF parameter B = 2 PDF mean = 1 PDF circular variance = 0.302225 Sample size = 1000 Sample mean = 1.01316 Sample circular variance = 0.307398 Sample maximum = 4.0905 Sample minimum = -2.04316 VON_MISES_SAMPLE_TEST Normal end of execution. WEIBULL_CDF_TEST Python version: 3.6.5 WEIBULL_CDF evaluates the Weibull CDF WEIBULL_CDF_INV inverts the Weibull CDF. WEIBULL_PDF evaluates the Weibull PDF PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 X PDF CDF CDF_INV 4.11372 0.364494 0.218418 4.11372 5.99057 0.137084 0.956318 5.99057 5.45985 0.348698 0.829509 5.45985 4.859 0.505816 0.561695 4.859 4.56772 0.488817 0.415307 4.56772 3.53425 0.166552 0.0661187 3.53425 4.21624 0.399093 0.257578 4.21624 3.75263 0.236621 0.109957 3.75263 3.38034 0.124184 0.043829 3.38034 5.00376 0.489885 0.633966 5.00376 WEIBULL_CDF_TEST Normal end of execution. WEIBULL_SAMPLE_TEST Python version: 3.6.5 WEIBULL_MEAN computes the Weibull mean WEIBULL_SAMPLE samples the Weibull distribution WEIBULL_VARIANCE computes the Weibull variance. PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 PDF mean = 4.71921 PDF variance = 0.581953 Sample size = 1000 Sample mean = 4.7225 Sample variance = 0.587748 Sample maximum = 6.72812 Sample minimum = 2.62134 WEIBULL_SAMPLE_TEST Normal end of execution. WEIBULL_DISCRETE_CDF_TEST Python version: 3.6.5 WEIBULL_DISCRETE_CDF evaluates the Weibull Discrete CDF WEIBULL_DISCRETE_CDF_INV inverts the Weibull Discrete CDF. WEIBULL_DISCRETE_PDF evaluates the Weibull Discrete PDF PDF parameter A = 0.5 PDF parameter B = 1.5 X PDF CDF CDF_INV 1 0.359214 0.859214 1 2 0.113508 0.972723 3 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 WEIBULL_DISCRETE_CDF_TEST Normal end of execution. WEIBULL_DISCRETE_SAMPLE_TEST Python version: 3.6.5 WEIBULL_DISCRETE_SAMPLE samples the Weibull Discrete distribution PDF parameter A = 0.5 PDF parameter B = 1.5 Sample size = 1000 Sample mean = 1.166 Sample variance = 0.208653 Sample maximum = 4 Sample minimum = 1 WEIBULL_DISCRETE_SAMPLE_TEST Normal end of execution. ZIPF_CDF_TEST Python version: 3.6.5 ZIPF_PDF evaluates the Zipf PDF. ZIPF_CDF evaluates the Zipf CDF. ZIPF_CDF_INV inverts the Zipf CDF. PDF parameter A = 2 X PDF(X) CDF(X) CDF_INV(CDF) 1 0.607927 0.607927 1 2 0.151982 0.759909 2 3 0.0675475 0.827456 3 4 0.0379954 0.865452 4 5 0.0243171 0.889769 5 6 0.0168869 0.906656 6 7 0.0124067 0.919062 7 8 0.00949886 0.928561 8 9 0.00750527 0.936067 9 10 0.00607927 0.942146 10 11 0.00502419 0.94717 11 12 0.00422172 0.951392 12 13 0.0035972 0.954989 13 14 0.00310167 0.958091 14 15 0.0027019 0.960792 15 16 0.00237472 0.963167 16 17 0.00210355 0.965271 17 18 0.00187632 0.967147 18 19 0.00168401 0.968831 19 20 0.00151982 0.970351 20 ZIPF_CDF_TEST Normal end of execution. ZIPF_SAMPLE_TEST Python version: 3.6.5 ZIPF_MEAN returns the mean of the Zipf distribution. ZIPF_SAMPLE samples the Zipf distribution. ZIPF_VARIANCE returns the variance of the Zipf distribution. PDF parameter A = 4 PDF mean = 1.11063 PDF variance = 0.286326 Sample size = 1000 Sample mean = 1.12 Sample variance = 0.197798 Sample maximum = 6 Sample minimum = 1 ZIPF_SAMPLE_TEST Normal end of execution. PROB_TEST: Normal end of execution. Thu Sep 13 13:01:35 2018