26 September 2018 01:49:07 PM PROB_TEST C++ version. Test the PROB library. ANGLE_CDF_TEST ANGLE_CDF evaluates the Angle CDF; Parameter N = 5 PDF argument X = 0.5 CDF value = 0.0107809 ANGLE_MEAN_TEST ANGLIT_MEAN computes the Angle mean; Parameter N = 5 PDF mean = 1.5708 ANGLE_PDF_TEST ANGLE_PDF evaluates the Angle PDF; Parameter N = 5 PDF argument X = 0.5 PDF value = 0.0826466 ANGLIT_CDF_TEST 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_SAMPLE_TEST 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 ARCSIN_CDF_TEST 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_SAMPLE_TEST 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 BENFORD_CDF_TEST BENFORD_CDF evaluates the Benford CDF. N CDF(N) CDF(N) by summing 1 0.30103 0.30103 0.30103 2 0.176091 0.477121 0.477121 3 0.124939 0.60206 0.60206 4 0.09691 0.69897 0.69897 5 0.0791812 0.778151 0.778151 6 0.0669468 0.845098 0.845098 7 0.0579919 0.90309 0.90309 8 0.0511525 0.954243 0.954243 9 0.0457575 1 1 N CDF(N) CDF(N) by summing 10 0.0413927 0.0413927 0.0413927 11 0.0377886 0.0791812 0.0791812 12 0.0347621 0.113943 0.113943 13 0.0321847 0.146128 0.146128 14 0.0299632 0.176091 0.176091 15 0.0280287 0.20412 0.20412 16 0.0263289 0.230449 0.230449 17 0.0248236 0.255273 0.255273 18 0.0234811 0.278754 0.278754 19 0.0222764 0.30103 0.30103 20 0.0211893 0.322219 0.322219 21 0.0202034 0.342423 0.342423 22 0.0193052 0.361728 0.361728 23 0.0184834 0.380211 0.380211 24 0.0177288 0.39794 0.39794 25 0.0170333 0.414973 0.414973 26 0.0163904 0.431364 0.431364 27 0.0157943 0.447158 0.447158 28 0.01524 0.462398 0.462398 29 0.0147233 0.477121 0.477121 30 0.0142404 0.491362 0.491362 31 0.0137883 0.50515 0.50515 32 0.013364 0.518514 0.518514 33 0.012965 0.531479 0.531479 34 0.0125891 0.544068 0.544068 35 0.0122345 0.556303 0.556303 36 0.0118992 0.568202 0.568202 37 0.0115819 0.579784 0.579784 38 0.011281 0.591065 0.591065 39 0.0109954 0.60206 0.60206 40 0.0107239 0.612784 0.612784 41 0.0104654 0.623249 0.623249 42 0.0102192 0.633468 0.633468 43 0.00998422 0.643453 0.643453 44 0.00975984 0.653213 0.653213 45 0.00954532 0.662758 0.662758 46 0.00934003 0.672098 0.672098 47 0.00914338 0.681241 0.681241 48 0.00895484 0.690196 0.690196 49 0.00877392 0.69897 0.69897 50 0.00860017 0.70757 0.70757 51 0.00843317 0.716003 0.716003 52 0.00827253 0.724276 0.724276 53 0.00811789 0.732394 0.732394 54 0.00796893 0.740363 0.740363 55 0.00782534 0.748188 0.748188 56 0.00768683 0.755875 0.755875 57 0.00755314 0.763428 0.763428 58 0.00742402 0.770852 0.770852 59 0.00729924 0.778151 0.778151 60 0.00717858 0.78533 0.78533 61 0.00706185 0.792392 0.792392 62 0.00694886 0.799341 0.799341 63 0.00683942 0.80618 0.80618 64 0.00673338 0.812913 0.812913 65 0.00663058 0.819544 0.819544 66 0.00653087 0.826075 0.826075 67 0.00643411 0.832509 0.832509 68 0.00634018 0.838849 0.838849 69 0.00624895 0.845098 0.845098 70 0.00616031 0.851258 0.851258 71 0.00607415 0.857332 0.857332 72 0.00599036 0.863323 0.863323 73 0.00590886 0.869232 0.869232 74 0.00582954 0.875061 0.875061 75 0.00575233 0.880814 0.880814 76 0.00567713 0.886491 0.886491 77 0.00560388 0.892095 0.892095 78 0.00553249 0.897627 0.897627 79 0.0054629 0.90309 0.90309 80 0.00539503 0.908485 0.908485 81 0.00532883 0.913814 0.913814 82 0.00526424 0.919078 0.919078 83 0.00520119 0.924279 0.924279 84 0.00513964 0.929419 0.929419 85 0.00507953 0.934498 0.934498 86 0.0050208 0.939519 0.939519 87 0.00496342 0.944483 0.944483 88 0.00490733 0.94939 0.94939 89 0.0048525 0.954243 0.954243 90 0.00479888 0.959041 0.959041 91 0.00474644 0.963788 0.963788 92 0.00469512 0.968483 0.968483 93 0.00464491 0.973128 0.973128 94 0.00459575 0.977724 0.977724 95 0.00454763 0.982271 0.982271 96 0.0045005 0.986772 0.986772 97 0.00445434 0.991226 0.991226 98 0.00440912 0.995635 0.995635 99 0.00436481 1 1 BENFORD_PDF_TEST 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 BERNOULLI_CDF_TEST 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_SAMPLE_TEST 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 BESSEL_I0_TEST: BESSEL_I0 evaluates the Bessel function of the first kind and order 0; X Exact F BESSEL_I0(X) 0 1 1 0.2 1.01003 1.01003 0.4 1.0404 1.0404 0.6 1.09205 1.09205 0.8 1.16651 1.16651 1 1.26607 1.26607 1.2 1.39373 1.39373 1.4 1.5534 1.5534 1.6 1.74998 1.74998 1.8 1.98956 1.98956 2 2.27959 2.27959 2.5 3.28984 3.28984 3 4.88079 4.88079 3.5 7.3782 7.3782 4 11.3019 11.3019 4.5 17.4812 17.4812 5 27.2399 27.2399 6 67.2344 67.2344 8 427.564 427.564 10 2815.72 2815.72 BESSEL_I1_TEST: BESSEL_I1 evaluates the Bessel function of the first kind and order 1; X Exact F BESSEL_I1(X) 0 0 0 0.2 0.100501 0.100501 0.4 0.204027 0.204027 0.6 0.313704 0.313704 0.8 0.432865 0.432865 1 0.565159 0.565159 1.2 0.714678 0.714678 1.4 0.886092 0.886092 1.6 1.08481 1.08481 1.8 1.31717 1.31717 2 1.59064 1.59064 2.5 2.51672 2.51672 3 3.95337 3.95337 3.5 6.20583 6.20583 4 9.75947 9.75947 4.5 15.3892 15.3892 5 24.3356 24.3356 6 61.3419 61.3419 8 399.873 399.873 10 2670.99 2670.99 BETA_BINOMIAL_CDF_TEST 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_SAMPLE_TEST 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_CDF_TEST 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 0.401337 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_INC_TEST: 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_SAMPLE_TEST 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 BINOMIAL_CDF_TEST 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_SAMPLE_TEST 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 BIRTHDAY_CDF_TEST BIRTHDAY_CDF evaluates the CDF; BIRTHDAY_CDF_INV inverts the CDF. BIRTHDAY_PDF evaluates the PDF; N PDF CDF CDF_INV 1 0 0 0 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_SAMPLE_TEST BIRTHDAY_SAMPLE samples the Birthday distribution. N Mean PDF 10 0.0264 0.0223243 11 0.0232 0.0241932 12 0.0244 0.0258834 13 0.0262 0.0273855 14 0.0283 0.0286922 15 0.0281 0.0297988 16 0.0314 0.0307027 17 0.0325 0.0314037 18 0.0315 0.0319038 19 0.0344 0.0322071 20 0.0332 0.0323199 21 0.0337 0.03225 22 0.0321 0.032007 23 0.0317 0.0316019 24 0.0302 0.031047 25 0.0303 0.0303554 26 0.0292 0.0295411 27 0.0316 0.0286185 28 0.0306 0.0276022 29 0.0263 0.0265071 30 0.0261 0.0253477 31 0.0231 0.0241384 32 0.0271 0.0228929 33 0.0209 0.0216243 34 0.0209 0.020345 35 0.0189 0.0190664 36 0.0189 0.0177989 37 0.0159 0.0165519 38 0.0163 0.0153338 39 0.0148 0.0141518 40 0.012 0.0130121 BRADFORD_CDF_TEST 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_SAMPLE_TEST 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 BUFFON_BOX_PDF_TEST tests BUFFON_BOX_PDF. 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_SAMPLE_TEST 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 10 3 0.141593 100 98 3.06122 0.0803682 10000 9557 3.13906 0.00253228 1000000 954728 3.14226 0.00066357 BUFFON_PDF_TEST 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_SAMPLE_TEST BUFFON_SAMPLE simulates a Buffon 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 4 5 1.85841 100 73 2.73973 0.401867 10000 6389 3.13038 0.0112123 1000000 637013 3.13965 0.0019393 BURR_CDF_TEST 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_SAMPLE_TEST BURR_MEAN computes the Burr mean; BURR_SAMPLE samples the Burr distribution; BURR_VARIANCE computes the Burr variance; 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 = 2.61414 Sample variance = 0.605821 Sample maximum = 6.50601 Sample minimum = 1.19455 CARDIOID_CDF_TEST 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_SAMPLE_TEST 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 CAUCHY_CDF_TEST 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_SAMPLE_TEST CAUCHY_MEAN computes the Cauchy mean; CAUCHY_SAMPLE samples the Cauchy distribution; CAUCHY_VARIANCE computes the Cauchy variance; PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 1e+30 Sample size = 1000 Sample mean = 1.66442 Sample variance = 1579.41 Sample maximum = 458.532 Sample minimum = -517.438 CHEBYSHEV1_CDF_TEST 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_SAMPLE_TEST 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 CHI_CDF_TEST 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_SAMPLE_TEST CHI_MEAN computes the Chi mean; CHI_SAMPLE samples the Chi distribution; CHI_VARIANCE computes the Chi variance; 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_SQUARE_CDF_TEST 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 0.816838 6.22214 8.25908 0.0332227 0.917464 8.25908 9.02741 0.0247301 0.939582 9.02741 4.13727 0.130694 0.612253 4.13727 0.703353 0.123704 0.0490852 0.703353 1.44998 0.175567 0.164536 1.44998 0.634817 0.115542 0.0408827 0.634817 8.54272 0.02982 0.926397 8.54272 13.0901 0.00470332 0.989156 13.0901 1.46095 0.175928 0.166465 1.46095 CHI_SQUARE_SAMPLE_TEST 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_NONCENTRAL_SAMPLE_TEST CHI_SQUARE_NONCENTRAL_MEAN computes the Chi Square Noncentral mean; CHI_SQUARE_NONCENTRAL_SAMPLE samples the Chi Square Noncentral distribution; 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 CIRCULAR_NORMAL_01_SAMPLE_TEST 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 mean = 0 0 PDF variance = 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_SAMPLE_TEST 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 mean = 1 5 PDF variance = 0.75 0.75 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 COSINE_CDF_TEST COSINE_CDF evaluates the Cosine CDF; COSINE_CDF_INV inverts the Cosine CDF. COSINE_PDF evaluates theCosine 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_SAMPLE_TEST 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 COUPON_COMPLETE_PDF_TEST COUPON_COMPLETE_PDF evaluates the coupon collector's complete collection 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_SAMPLE_TEST: COUPON_SAMPLE samples the coupon PDF. Number of coupon types is 5 Expected wait is about 8.04719 1 10 2 8 3 14 4 7 5 10 6 11 7 17 8 11 9 6 10 12 Average wait was 10.6 Number of coupon types is 10 Expected wait is about 23.0259 1 29 2 31 3 47 4 42 5 27 6 31 7 44 8 23 9 11 10 30 Average wait was 31.5 Number of coupon types is 15 Expected wait is about 40.6208 1 65 2 31 3 60 4 51 5 46 6 37 7 51 8 40 9 52 10 52 Average wait was 48.5 Number of coupon types is 20 Expected wait is about 59.9146 1 80 2 80 3 51 4 54 5 58 6 80 7 173 8 69 9 156 10 54 Average wait was 85.5 Number of coupon types is 25 Expected wait is about 80.4719 1 117 2 188 3 95 4 77 5 168 6 110 7 128 8 77 9 103 10 82 Average wait was 114.5 DERANGED_CDF_TEST 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_SAMPLE_TEST DERANGED_MEAN computes the Deranged mean; DERANGED_SAMPLE samples the Deranged distribution; DERANGED_VARIANCE computes the Deranged variance. 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 DIPOLE_CDF_TEST 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 -2.00376 0.0538127 0.131477 -2.00293 1.90221 0.060188 0.828708 1.90332 9.07094 0.00368677 0.964094 9.09375 0.244458 0.316631 0.501226 0.244629 0.203988 0.317466 0.487654 0.204102 -10.6175 0.00288846 0.029192 -10.6211 -0.86502 0.226546 0.227479 -0.865234 2.15741 0.0463925 0.847767 2.15674 -4.81123 0.0129237 0.0619356 -4.81836 0.646407 0.273715 0.626535 0.646484 PDF parameter A = 1.5708 PDF parameter B = 0 X PDF CDF CDF_INV -0.904508 0.175075 0.265947 -0.904297 -0.843581 0.185969 0.276943 -0.84375 0.227018 0.302709 0.571058 0.227051 -0.320266 0.288698 0.401342 -0.320312 -0.506838 0.253253 0.35068 -0.506836 0.251535 0.299369 0.578439 0.251465 -0.177728 0.308563 0.444012 -0.177734 -0.386329 0.276972 0.38265 -0.38623 -0.0852594 0.316013 0.472927 -0.0849609 -1.51135 0.0969218 0.186061 -1.51074 DIPOLE_SAMPLE_TEST 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 DIRICHLET_SAMPLE DIRICHLET_MEAN computes the Dirichlet mean; DIRICHLET_SAMPLE samples the Dirichlet distribution; DIRICHLET_VARIANCE computes the Dirichlet variance; Number of components N = 3 PDF parameter A: 0: 0.25 1: 0.5 2: 1.25 PDF mean: 0: 0.125 1: 0.25 2: 0.625 PDF variance: 0: 0.0364583 1: 0.0625 2: 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 Component Mean, Variance, Min, Max: 0 0.128337 0.0377062 0.975128 4.0796e-11 1 0.23718 0.0592189 0.976032 1.30377e-06 2 0.634483 0.0751289 0.999945 0.000245466 DIRICHLET_PDF_TEST DIRICHLET_PDF evaluates the Dirichlet PDF; Number of components N = 3 PDF parameter A: 0: 0.25 1: 0.5 2: 1.25 PDF argument X: 0: 0.5 1: 0.125 2: 0.375 PDF value = 0.63907 DIRICHLET_MIX_SAMPLE_TEST 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 Component Mean, Variance, Max, Min: 0 0.278716 0.0546592 0.986951 3.62858e-10 1 0.170222 0.0397946 0.993637 5.84186e-08 2 0.551062 0.062022 0.998934 0.00518575 DIRICHLET_MIX_PDF_TEST 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 argument X: 0: 0.5 1: 0.125 2: 0.375 PDF value = 2.12288 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 parameter 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_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 parameter 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 DISK_SAMPLE DISK_MEAN returns the Disk mean; DISK_SAMPLE samples the Disk distribution; DISK_VARIANCE returns the Disk variance; PDF parameter A = 10 PDF parameter B = 4 PDF parameter C = 3 Disk mean = 10 4 Disk variance = 4.5 Sample size = 1000 Sample mean = 9.99926 4.06034 Sample variance = 4.48099 Sample maximum = 12.9218 6.96697 Sample minimum = 7.04381 1.03574 EMPIRICAL_DISCRETE_CDF_TEST 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_SAMPLE_TEST 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 ENGLISH_LETTER_CDF_TEST 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_SENTENCE_LENGTH_CDF_TEST 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_SAMPLE_TEST 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_WORD_LENGTH_CDF_TEST ENGLISH_WORD_LENGTH_CDF evaluates the English Word LengthCDF; ENGLISH_WORD_LENGTH_CDF_INV inverts the English Word LengthCDF. ENGLISH_WORD_LENGTH_PDF evaluates the English Word LengthPDF; 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_SAMPLE_TEST ENGLISH_WORD_LENGTH_MEAN computes the English Word Lengthmean; ENGLISH_WORD_LENGTH_SAMPLE samples the English Word Lengthdistribution; ENGLISH_WORD_LENGTH_VARIANCE computes the English Word Lengthvariance. 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 ERLANG_CDF_TEST 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_SAMPLE_TEST 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 EXPONENTIAL_CDF_TEST 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_SAMPLE_TEST 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_01_CDF_TEST 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 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 EXTREME_VALUES_CDF_TEST 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_SAMPLE_TEST 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 F_CDF_TEST F_CDF evaluates the F CDF; F_PDF evaluates the F PDF; F_SAMPLE samples the F PDF; PDF parameter M = 1 PDF parameter N = 1 X PDF CDF 8.79828 0.0109522 0.792993 0.913042 0.174133 0.485526 0.552007 0.276048 0.406792 0.00347467 5.38129 0.037483 0.0161641 2.46383 0.0805067 0.0212137 2.14006 0.0920758 1.26646 0.124798 0.537509 0.00713115 3.74269 0.0536328 2.23222 0.0659146 0.624499 0.060063 1.22522 0.153005 F_SAMPLE_TEST 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 FERMI_DIRAC_SAMPLE_TEST FERMI_DIRAC_SAMPLE samples the Fermi Dirac distribution. U = 1 V = 1 Sample size = 0.595778 Sample mean = 0.595778 Sample variance = 0.175762 Sample maximum = 2.59989 Sample minimum = 9.85564e-05 U = 2 V = 1 Sample size = 1.04686 Sample mean = 1.04686 Sample variance = 0.43191 Sample maximum = 3.51644 Sample minimum = 0.000187922 U = 4 V = 1 Sample size = 2.01803 Sample mean = 2.01803 Sample variance = 1.43756 Sample maximum = 5.40369 Sample minimum = 0.000375606 U = 8 V = 1 Sample size = 3.99861 Sample mean = 3.99861 Sample variance = 5.45539 Sample maximum = 9.26709 Sample minimum = 0.000751212 U = 16 V = 1 Sample size = 7.97895 Sample mean = 7.97895 Sample variance = 21.5306 Sample maximum = 17.1139 Sample minimum = 0.00150242 U = 32 V = 1 Sample size = 15.949 Sample mean = 15.949 Sample variance = 85.8381 Sample maximum = 32.9504 Sample minimum = 0.00300485 U = 1 V = 0.25 Sample size = 0.504508 Sample mean = 0.504508 Sample variance = 0.0898473 Sample maximum = 1.35092 Sample minimum = 9.39015e-05 FISHER_SAMPLE_TEST FISHER_PDF evaluates the Fisher PDF. PDF parameters: Concentration parameter KAPPA = 0 Direction MU(1:3) = 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 Direction MU(1:3) = 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 Direction MU(1:3) = 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 FISK_CDF_TEST 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_SAMPLE_TEST 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 FOLDED_NORMAL_CDF_TEST 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_SAMPLE_TEST 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 FRECHET_CDF_TEST 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 0.869476 1.14652 0.218418 0.869476 2.81845 0.0454656 0.956318 2.81845 1.74896 0.265962 0.829509 1.74896 1.20132 0.809067 0.561695 1.20132 1.04403 1.04866 0.415307 1.04403 0.716705 0.751767 0.0661187 0.716705 0.903373 1.16028 0.257578 0.903373 0.76799 0.948247 0.109957 0.76799 0.683811 0.601365 0.043829 0.683811 1.29943 0.667067 0.633966 1.29943 FRECHET_SAMPLE_TEST 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 GAMMA_CDF_TEST GAMMA_CDF evaluates the Gamma CDF; GAMMA_PDF evaluates the Gamma PDF; GAMMA_SAMPLE samples the Gamma PDF; PDF parameter A = 1 PDF parameter B = 1.5 PDF parameter B = 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_SAMPLE_TEST GAMMA_MEAN computes the Gamma mean; GAMMA_SAMPLE samples the Gamma distribution; GAMMA_VARIANCE computes the Gamma variance; 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 GENLOGISTIC_CDF_TEST GENLOGISTIC_CDF evaluates the Genlogistic CDF; GENLOGISTIC_CDF_INV inverts the Genlogistic CDF. GENLOGISTIC_PDF evaluates the Genlogistic PDF; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 1.82954 0.13032 0.218418 1.82954 9.39944 0.0211989 0.956318 9.39944 6.48873 0.0751605 0.829509 6.48873 4.10241 0.147371 0.561695 4.10241 3.15571 0.158177 0.415307 3.15571 0.22539 0.0590738 0.0661187 0.22539 2.11836 0.140536 0.257578 2.11836 0.832536 0.0859182 0.109957 0.832536 -0.215463 0.0425639 0.043829 -0.215463 4.61496 0.13403 0.633966 4.61496 GENLOGISTIC_SAMPLE_TEST GENLOGISTIC_MEAN computes the Genlogistic mean; GENLOGISTIC_SAMPLE samples the Genlogistic distribution; GENLOGISTIC_VARIANCE computes the Genlogistic variance; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 4 PDF variance = 8.15947 Sample size = 1000 Sample mean = 4.00819 Sample variance = 8.13473 Sample maximum = 15.534 Sample minimum = -2.93789 GEOMETRIC_CDF_TEST 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_SAMPLE_TEST 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 GOMPERTZ_CDF_TEST 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_SAMPLE_TEST GOMPERTZ_MEAN computes the Gompertz mean; GOMPERTZ_SAMPLE samples the Gompertz distribution; GOMPERTZ_VARIANCE computes the Gompertz variance; 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 GUMBEL_CDF_TEST 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_SAMPLE_TEST 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 HALF_NORMAL_CDF_TEST 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_SAMPLE_TEST 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 HYPERGEOMETRIC_CDF_TEST HYPERGEOMETRIC_CDF evaluates the Hypergeometric CDF. HYPERGEOMETRIC_PDF evaluates the Hypergeometric PDF. Total number of balls L = 100 Number of white balls M = 7 Number of balls taken N = 10 PDF argument X = 7 PDF value = = 7.49646e-09 CDF value = = 1 HYPERGEOMETRIC_SAMPLE_TEST HYPERGEOMETRIC_MEAN computes the Hypergeometric mean; HYPERGEOMETRIC_SAMPLE samples the Hypergeometric distribution; HYPERGEOMETRIC_VARIANCE computes the Hypergeometric variance. Total number of balls L = 100 Number of white balls M = 7 Number of balls taken N = 10 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 I4_CHOOSE_TEST 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_LOG_TEST 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_IS_POWER_OF_10_TEST I4_IS_POWER_OF_10 reports whether an I4 is a power of 10. I I4_IS_POWER_OF_10(I) 97 0 98 0 99 0 100 1 101 0 102 0 103 0 I4_UNIFORM_AB_TEST 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 I4VEC_UNIFORM_AB_NEW_TEST I4VEC_UNIFORM_AB_NEW 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_UNIQUE_COUNT_TEST I4VEC_UNIQUE_COUNT counts unique entries in an I4VEC. Array: 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 INVERSE_GAUSSIAN_CDF_TEST 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_SAMPLE_TEST 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 LAPLACE_CDF_TEST 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_SAMPLE_TEST 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 LEVY_CDF_TEST 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 LOGISTIC_CDF_TEST 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_SAMPLE_TEST 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 LOG_NORMAL_CDF_TEST 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_SAMPLE_TEST 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_SERIES_CDF_TEST 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_SAMPLE_TEST LOG_SERIES_MEAN computes the Log Series mean; LOG_SERIES_SAMPLE samples the Log Series distribution; LOG_SERIES_VARIANCE computes the Log Series variance. 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_UNIFORM_CDF_TEST 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_SAMPLE_TEST LOG_UNIFORM_MEAN computes the Log Uniform mean; LOG_UNIFORM_SAMPLE samples the Log Uniform distribution; PDF parameter A = 2 PDF parameter B = 20 PDF mean = 7.8173 Sample size = 1000 Sample mean = 7.8421 Sample variance = 24.5202 Sample maximum = 19.9039 Sample minimum = 2.00848 LORENTZ_CDF_TEST 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_SAMPLE_TEST LORENTZ_MEAN computes the Lorentz mean; LORENTZ_SAMPLE samples the Lorentz distribution; LORENTZ_VARIANCE computes the Lorentz variance. 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 MAXWELL_CDF_TEST8 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_SAMPLE_TEST MAXWELL_MEAN computes the Maxwell mean; MAXWELL_SAMPLE samples the Maxwell distribution; MAXWELL_VARIANCE computes the Maxwell variance. PDF parameter A = 2 PDF mean = 3.19154 PDF variance = 1.81408 Sample size = 1000 Sample mean = 3.15337 Sample variance = 1.9332 Sample maximum = 8.32689 Sample minimum = 0.206015 MULTINOMIAL_TEST 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_SAMPLE_TEST 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 mean: 0: 0.625 1: 2.5 2: 1.875 PDF variance: 0: 0.546875 1: 1.25 2: 1.17188 Sample size = 1000 Component Mean, Variance, Min, Max: 1 0.628 0.552168 0 3 2 2.472 1.23445 0 5 3 1.9 1.20721 0 5 MULTINOMIAL_PDF_TEST MULTINOMIAL_PDF evaluates the Multinomial PDF; PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 0: 0.1 1: 0.5 2: 0.4 PDF argument X: 0: 0 1: 2 2: 3 PDF value = 0.16 MULTINOULLI_PDF_TEST MULTINOULLI_PDF evaluates the Multinoulli PDF. X pdf(X) -1 0 0 0.0732641 1 0.320778 2 0.278242 3 0.18841 4 0.139306 5 0 NAKAGAMI_CDF_TEST NAKAGAMI_CDF evaluates the Nakagami CDF; NAKAGAMI_CDF_INV inverts the Nakagami CDF; NAKAGAMI_PDF evaluates the Nakagami PDF; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 1.36515 0.002478 0.000154653 1.36515 1.5164 0.0126837 0.00114848 1.5164 1.63246 0.0316261 0.00359949 1.63246 1.7303 0.0587439 0.00792633 1.7303 1.8165 0.0928557 0.0143877 1.8165 1.89443 0.132535 0.0231153 1.89443 1.96609 0.176307 0.0341416 1.96609 2.0328 0.222751 0.0474226 2.0328 2.09545 0.270565 0.0628569 2.09545 2.1547 0.318593 0.0803014 2.1547 NAKAGAMI_SAMPLE_TEST NAKAGAMI_MEAN evaluates the Nakagami mean; NAKAGAMI_VARIANCE evaluates the Nakagami variance; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 2.91874 PDF variance = 0.318446 NEGATIVE_BINOMIAL_CDF_TEST 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_SAMPLE_TEST 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 NORMAL_01_CDF_TEST 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 1.679040256736491 0.0974392 0.953428 1.679040256746338 -0.5660598123302577 0.339884 0.285677 -0.5660598123353983 1.21293421737931 0.191179 0.887423 1.212934217394378 1.269380628984426 0.178244 0.897847 1.269380629005457 -1.666086672831968 0.0995733 0.0478481 -1.666086672843646 -2.242464038261558 0.0322815 0.0124657 -2.242464038262084 0.0396749185148341 0.398628 0.515824 0.03967491851894145 0.6730681958483083 0.318081 0.749548 0.6730681958595057 -0.2751273507132183 0.384125 0.391609 -0.2751273507160336 2.164004788036971 0.0383732 0.984768 2.164004788031278 NORMAL_01_SAMPLES_TEST NORMAL_01_MEAN computes the Normal 01 mean; NORMAL_01_SAMPLES samples the Normal 01 distribution; NORMAL_01_VARIANCE computes the Normal 01 variance; PDF mean = 0 PDF variance = 1 Sample size = 1000 Sample mean = 0.0266326 Sample variance = 0.974766 Sample maximum = 3.54448 Sample minimum = -2.93051 NORMAL_CDF_TEST NORMAL_CDF evaluates the Normal CDF; NORMAL_CDF_INV inverts the Normal CDF. NORMAL_PDF evaluates the Normal PDF; PDF parameter MU = 100 PDF parameter SIGMA = 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_SAMPLES_TEST NORMAL_MEAN computes the Normal mean; NORMAL_SAMPLES samples the Normal distribution; NORMAL_VARIANCE computes the Normal variance; PDF parameter MU= 100 PDF parameter SIGMA = 15 PDF mean = 100 PDF variance = 225 Sample size = 1000 Sample mean = 100.399 Sample variance = 219.322 Sample maximum = 153.167 Sample minimum = 56.0424 NORMAL_TRUNCATED_AB_CDF_TEST 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_SAMPLE_TEST 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_A_CDF_TEST 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_SAMPLE_TEST 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_B_CDF_TEST 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_SAMPLE_TEST 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 PARETO_CDF_TEST 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_SAMPLE_TEST 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 PEARSON_05_PDF PEARSON_05_PDF evaluates the Pearson 05 PDF. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF argument X = 5 PDF value = 0.0758163 PLANCK_PDF_TEST PLANCK_PDF evaluates the Planck PDF. PLANCK_SAMPLE samples 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_SAMPLE_TEST PLANCK_MEAN computes the Planck mean; PLANCK_SAMPLE samples the Planck distribution; PLANCK_VARIANCE computes the Planck variance; PDF parameter A = 2 PDF parameter B = 3 PDF mean = 3.83223 PDF variance = 0 Sample size = 1000 Sample mean = 1.93308 Sample variance = 0.99989 Sample maximum = 6.48678 Sample minimum = 0.165955 POISSON_CDF_TEST 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_SAMPLE_TEST POISSON_SAMPLE samples the Poisson PDF. POISSON_SAMPLE samples the Poisson PDF. POISSON_SAMPLE samples the Poisson PDF. 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 POWER_CDF_TEST 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_SAMPLE_TEST 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 QUASIGEOMETRIC_CDF_TEST 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_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 mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.267 Sample variance = 3.21693 Sample maximum = 11 Sample minimum = 0 R8_BETA_TEST: R8_BETA evaluates the Beta function. X Y BETA(X,Y) R8_BETA(X,Y) tabulated computed. 0.2 1 5 4.999999999999998 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 4.999999999999998 1 0.4 2.5 2.5 1 1 1 1 2 2 0.1666666666666667 0.1666666666666667 3 3 0.03333333333333333 0.03333333333333335 4 4 0.007142857142857143 0.007142857142857152 5 5 0.001587301587301587 0.001587301587301586 6 2 0.02380952380952381 0.02380952380952384 6 3 0.005952380952380952 0.005952380952380948 6 4 0.001984126984126984 0.001984126984126982 6 5 0.0007936507936507937 0.0007936507936507921 6 6 0.0003607503607503608 0.0003607503607503604 7 7 8.325008325008325e-05 8.325008325008344e-05 R8_CEILING_TEST R8_CEILING rounds an R8 up. X R8_CEILING(X) -1.2 -1 -1 -1 -0.8 0 -0.6 0 -0.4 0 -0.2 0 0 0 0.2 1 0.4 1 0.6 1 0.8 1 1 1 1.2 2 R8_ERROR_F_TEST R8_ERROR_F evaluates ERF(X). X -> Y = R8_ERROR_F(X) -> Z = R8_ERROR_F_INVERSE(Y) 1.67904 0.982428 1.67904 -0.56606 -0.576596 -0.56606 1.21293 0.913719 1.21293 1.26938 0.927374 1.26938 -1.66609 -0.981537 -1.66609 -2.24246 -0.998483 -2.24246 0.0396749 0.0447449 0.0396749 0.673068 0.658833 0.673068 -0.275127 -0.30279 -0.275127 2.164 0.997789 2.164 0.297785 0.326341 0.297785 2.04454 0.996165 2.04454 1.39882 0.952097 1.39882 -1.24299 -0.921226 -1.24299 -0.0670837 -0.0755824 -0.0670837 -0.794396 -0.738752 -0.794396 -0.523768 -0.541137 -0.523768 -0.350567 -0.379948 -0.350567 0.1317 0.147753 0.1317 0.53738 0.552727 0.53738 R8_FACTORIAL_TEST R8_FACTORIAL evaluates the factorial function. I R8_FACTORIAL(I) 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 R8_GAMMA_INC_TEST: R8_GAMMA_INC evaluates the normalized incomplete Gamma function. 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_LOG_INT_TEST 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_UNIFORM_01_TEST R8_UNIFORM_01 samples a uniform random distribution in [0,1]. distributed random numbers. Using initial random number seed = 123456789 First few values: 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 Number of samples was 1000 Minimum value was 0.00183837 Maximum value was 0.997908 Average value was 0.50304 Variance was 0.082332 R8_ZETA_TEST R8_ZETA estimates the Zeta function. P R8_Zeta(P) 1 1e+30 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 RAYLEIGH_CDF_TEST 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_SAMPLE_TEST 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 RECIPROCAL_CDF_TEST 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_SAMPLE_TEST 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 RUNS_PDF_TEST RUNS_PDF evaluates the Runs PDF; M is the number of symbols of one kind, N is the number of symbols of the other kind, R is the number of runs (sequences of one symbol) M N R PDF 6 0 1 1 6 0 2 0 6 1 6 1 1 0 6 1 2 0.285714 6 1 3 0.714286 6 1 4 0 6 1 6 2 1 0 6 2 2 0.0714286 6 2 3 0.214286 6 2 4 0.357143 6 2 5 0.357143 6 2 6 0 6 1 6 3 1 0 6 3 2 0.0238095 6 3 3 0.0833333 6 3 4 0.238095 6 3 5 0.297619 6 3 6 0.238095 6 3 7 0.119048 6 3 8 0 6 1 6 4 1 0 6 4 2 0.00952381 6 4 3 0.0380952 6 4 4 0.142857 6 4 5 0.214286 6 4 6 0.285714 6 4 7 0.190476 6 4 8 0.0952381 6 4 9 0.0238095 6 4 10 0 6 1 6 5 1 0 6 5 2 0.004329 6 5 3 0.0194805 6 5 4 0.0865801 6 5 5 0.151515 6 5 6 0.25974 6 5 7 0.21645 6 5 8 0.17316 6 5 9 0.0649351 6 5 10 0.021645 6 5 11 0.0021645 6 5 12 0 6 1 6 6 1 0 6 6 2 0.0021645 6 6 3 0.0108225 6 6 4 0.0541126 6 6 5 0.108225 6 6 6 0.21645 6 6 7 0.21645 6 6 8 0.21645 6 6 9 0.108225 6 6 10 0.0541126 6 6 11 0.0108225 6 6 12 0.0021645 6 6 13 0 6 6 14 0 6 1 6 7 1 0 6 7 2 0.0011655 6 7 3 0.00641026 6 7 4 0.034965 6 7 5 0.0786713 6 7 6 0.174825 6 7 7 0.203963 6 7 8 0.2331 6 7 9 0.145688 6 7 10 0.0874126 6 7 11 0.0262238 6 7 12 0.00699301 6 7 13 0.000582751 6 7 14 0 6 1 6 8 1 0 6 8 2 0.000666001 6 8 3 0.003996 6 8 4 0.02331 6 8 5 0.0582751 6 8 6 0.13986 6 8 7 0.18648 6 8 8 0.2331 6 8 9 0.174825 6 8 10 0.11655 6 8 11 0.04662 6 8 12 0.013986 6 8 13 0.002331 6 8 14 0 6 1 6 9 1 0 6 9 2 0.0003996 6 9 3 0.0025974 6 9 4 0.015984 6 9 5 0.043956 6 9 6 0.111888 6 9 7 0.167832 6 9 8 0.223776 6 9 9 0.195804 6 9 10 0.13986 6 9 11 0.0699301 6 9 12 0.0223776 6 9 13 0.00559441 6 9 14 0 6 1 RUNS_SAMPLE_TEST RUNS_MEAN computes the Runs mean; RUNS_SAMPLE samples the Runs distribution; RUNS_VARIANCE computes the Runs variance PDF parameter M = 10 PDF parameter N = 5 PDF mean = 7.66667 PDF variance = 2.69841 Sample size = 1000 Sample mean = 7.65 Sample variance = 2.61011 Sample maximum = 11 Sample minimum = 2 SECH_CDF_TEST 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_SAMPLE_TEST 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 SEMICIRCULAR_CDF_TEST 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_SAMPLE_TEST 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 STUDENT_CDF_TEST STUDENT_CDF evaluates the Student CDF; STUDENT_PDF evaluates the Student PDF; STUDENT_SAMPLE samples the Student PDF; PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 X PDF CDF 1.23384 0.331326 0.636863 0.763175 0.37563 0.550194 0.320752 0.379419 0.465751 -2.11984 0.0746224 0.119069 0.50983 0.382723 0.501881 3.93888 0.0283131 0.931835 0.985322 0.359192 0.591825 -0.714645 0.259709 0.282948 0.144113 0.36986 0.432312 0.464835 0.382605 0.493271 STUDENT_SAMPLE_TEST STUDENT_MEAN evaluates the Student mean; STUDENT_SAMPLE samples the Student PDF; 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_NONCENTRAL_CDF_TEST 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 TFN_TEST 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 TRIANGLE_CDF_TEST 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_SAMPLE_TEST TRIANGLE_MEAN computes the Triangle mean; TRIANGLE_SAMPLE samples the Triangle distribution; TRIANGLE_VARIANCE computes the Triangle variance; PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 10 PDF mean = 4.66667 PDF variance = 3.72222 Sample size = 1000 Sample mean = 4.67684 Sample variance = 3.70549 Sample maximum = 9.63699 Sample minimum = 1.18191 TRIANGULAR_CDF_TEST 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_SAMPLE_TEST 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 UNIFORM_01_CDF_TEST 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_ORDER_SAMPLE_TEST For the Uniform 01 Order PDF: UNIFORM_ORDER_SAMPLE samples. 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_SAMPLE_TEST 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_CDF_TEST 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_SAMPLE_TEST 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_DISCRETE_CDF_TEST 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 6 0.166667 1 6 4 0.166667 0.666667 5 3 0.166667 0.5 4 1 0.166667 0.166667 2 3 0.166667 0.5 4 2 0.166667 0.333333 3 1 0.166667 0.166667 2 5 0.166667 0.833333 6 UNIFORM_DISCRETE_SAMPLE_TEST 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 = 3.945 Sample variance = 2.70068 Sample maximum = 6 Sample minimum = 1 UNIFORM_NSPHERE_SAMPLE_TEST UNIFORM_NSPHERE_SAMPLE samples the Uniform Nsphere distribution. Dimension N of sphere = 3 Points on the sphere: 1 0.781938 -0.263617 0.56487 2 0.413678 -0.542961 -0.730797 3 0.0544828 0.924277 -0.377813 4 0.723278 0.0995291 0.683347 5 0.747038 -0.663815 -0.035826 6 -0.78339 -0.516512 -0.34571 7 0.146773 0.598886 -0.78727 8 -0.649577 -0.399299 -0.647001 9 0.375237 -0.770087 0.51591 10 -0.408985 0.0579096 -0.910702 VON_MISES_CDF_TEST 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_SAMPLE_TEST 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 WEIBULL_CDF_TEST 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_SAMPLE_TEST 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_DISCRETE_CDF_TEST 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 0 0.5 0.5 0 2 0.113508 0.972723 2 1 0.359214 0.859214 1 1 0.359214 0.859214 1 0 0.5 0.5 0 0 0.5 0.5 0 0 0.5 0.5 0 0 0.5 0.5 0 0 0.5 0.5 0 1 0.359214 0.859214 1 WEIBULL_DISCRETE_SAMPLE_TEST WEIBULL_DISCRETE_SAMPLE samples the Weibull Discrete distribution; PDF parameter A = 0.5 PDF parameter B = 1.5 Sample size = 1000 Sample mean = 0.676 Sample variance = 0.621646 Sample maximum = 4 Sample minimum = 0 ZIPF_CDF_TEST ZIPF_CDF evaluates the Zipf CDF; ZIPF_CDF_INV inverts the Zipf CDF; ZIPF_PDF evaluates the Zipf PDF; PDF parameter A = 2 X PDF CDF CDF_INV() 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_SAMPLE_TEST ZIPF_MEAN computes the Zipf mean; ZIPF_SAMPLE samples the Zipf distribution; ZIPF_VARIANCE computes the Zipf variance. 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 PROB_TEST Normal end of execution. 26 September 2018 01:49:08 PM