#! /usr/bin/env python # def beta_cdf_values ( n_data ): #*****************************************************************************80 # ## BETA_CDF_VALUES returns some values of the Beta CDF. # # Discussion: # # The incomplete Beta function may be written # # BETA_INC(A,B,X) = Integral (0 to X) T^(A-1) * (1-T)^(B-1) dT # / Integral (0 to 1) T^(A-1) * (1-T)^(B-1) dT # # Thus, # # BETA_INC(A,B,0.0) = 0.0; # BETA_INC(A,B,1.0) = 1.0 # # The incomplete Beta function is also sometimes called the # "modified" Beta function, or the "normalized" Beta function # or the Beta CDF (cumulative density function). # # In Mathematica, the function can be evaluated by: # # BETA[X,A,B] / BETA[A,B] # # The function can also be evaluated by using the Statistics package: # # Needs["Statistics`ContinuousDistributions`"] # dist = BetaDistribution [ a, b ] # CDF [ dist, x ] # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 15 January 2015 # # Author: # # John Burkardt # # Reference: # # Milton Abramowitz and Irene Stegun, # Handbook of Mathematical Functions, # US Department of Commerce, 1964. # # Karl Pearson, # Tables of the Incomplete Beta Function, # Cambridge University Press, 1968. # # Stephen Wolfram, # The Mathematica Book, # Fourth Edition, # Wolfram Media / Cambridge University Press, 1999. # # Parameters: # # Input/output, integer N_DATA. The user sets N_DATA to 0 before the # first call. On each call, the routine increments N_DATA by 1, and # returns the corresponding data; when there is no more data, the # output value of N_DATA will be 0 again. # # Output, real A, B, the parameters of the function. # # Output, real X, the argument of the function. # # Output, real F, the value of the function. # import numpy as np n_max = 45 a_vec = np.array ( ( \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 1.0E+00, \ 1.0E+00, \ 1.0E+00, \ 1.0E+00, \ 1.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 5.5E+00, \ 10.0E+00, \ 10.0E+00, \ 10.0E+00, \ 10.0E+00, \ 20.0E+00, \ 20.0E+00, \ 20.0E+00, \ 20.0E+00, \ 20.0E+00, \ 30.0E+00, \ 30.0E+00, \ 40.0E+00, \ 0.1E+01, \ 0.1E+01, \ 0.1E+01, \ 0.1E+01, \ 0.1E+01, \ 0.1E+01, \ 0.1E+01, \ 0.1E+01, \ 0.2E+01, \ 0.3E+01, \ 0.4E+01, \ 0.5E+01, \ 1.30625, \ 1.30625, \ 1.30625 )) b_vec = np.array ( ( \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 1.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 2.0E+00, \ 5.0E+00, \ 0.5E+00, \ 5.0E+00, \ 5.0E+00, \ 10.0E+00, \ 5.0E+00, \ 10.0E+00, \ 10.0E+00, \ 20.0E+00, \ 20.0E+00, \ 10.0E+00, \ 10.0E+00, \ 20.0E+00, \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 0.5E+00, \ 0.2E+01, \ 0.3E+01, \ 0.4E+01, \ 0.5E+01, \ 0.2E+01, \ 0.2E+01, \ 0.2E+01, \ 0.2E+01, \ 11.7562, \ 11.7562, \ 11.7562 )) f_vec = np.array ( ( \ 0.6376856085851985E-01, \ 0.2048327646991335E+00, \ 0.1000000000000000E+01, \ 0.0000000000000000E+00, \ 0.5012562893380045E-02, \ 0.5131670194948620E-01, \ 0.2928932188134525E+00, \ 0.5000000000000000E+00, \ 0.2800000000000000E-01, \ 0.1040000000000000E+00, \ 0.2160000000000000E+00, \ 0.3520000000000000E+00, \ 0.5000000000000000E+00, \ 0.6480000000000000E+00, \ 0.7840000000000000E+00, \ 0.8960000000000000E+00, \ 0.9720000000000000E+00, \ 0.4361908850559777E+00, \ 0.1516409096347099E+00, \ 0.8978271484375000E-01, \ 0.1000000000000000E+01, \ 0.5000000000000000E+00, \ 0.4598773297575791E+00, \ 0.2146816102371739E+00, \ 0.9507364826957875E+00, \ 0.5000000000000000E+00, \ 0.8979413687105918E+00, \ 0.2241297491808366E+00, \ 0.7586405487192086E+00, \ 0.7001783247477069E+00, \ 0.5131670194948620E-01, \ 0.1055728090000841E+00, \ 0.1633399734659245E+00, \ 0.2254033307585166E+00, \ 0.3600000000000000E+00, \ 0.4880000000000000E+00, \ 0.5904000000000000E+00, \ 0.6723200000000000E+00, \ 0.2160000000000000E+00, \ 0.8370000000000000E-01, \ 0.3078000000000000E-01, \ 0.1093500000000000E-01, \ 0.918884684620518, \ 0.21052977489419, \ 0.1824130512500673 ) ) x_vec = np.array ( ( \ 0.01E+00, \ 0.10E+00, \ 1.00E+00, \ 0.00E+00, \ 0.01E+00, \ 0.10E+00, \ 0.50E+00, \ 0.50E+00, \ 0.10E+00, \ 0.20E+00, \ 0.30E+00, \ 0.40E+00, \ 0.50E+00, \ 0.60E+00, \ 0.70E+00, \ 0.80E+00, \ 0.90E+00, \ 0.50E+00, \ 0.90E+00, \ 0.50E+00, \ 1.00E+00, \ 0.50E+00, \ 0.80E+00, \ 0.60E+00, \ 0.80E+00, \ 0.50E+00, \ 0.60E+00, \ 0.70E+00, \ 0.80E+00, \ 0.70E+00, \ 0.10E+00, \ 0.20E+00, \ 0.30E+00, \ 0.40E+00, \ 0.20E+00, \ 0.20E+00, \ 0.20E+00, \ 0.20E+00, \ 0.30E+00, \ 0.30E+00, \ 0.30E+00, \ 0.30E+00, \ 0.225609, \ 0.0335568, \ 0.0295222 ) ) if ( n_data < 0 ): n_data = 0 if ( n_max <= n_data ): n_data = 0 a = 0.0 b = 0.0 x = 0.0 f = 0.0 else: a = a_vec[n_data] b = b_vec[n_data] x = x_vec[n_data] f = f_vec[n_data] n_data = n_data + 1 return n_data, a, b, x, f def beta_cdf_values_test ( ): #*****************************************************************************80 # ## BETA_CDF_VALUES_TEST demonstrates the use of BETA_CDF_VALUES. # # Licensing: # # This code is distributed under the GNU LGPL license. # # Modified: # # 15 January 2015 # # Author: # # John Burkardt # import platform print ( '' ) print ( 'BETA_CDF_VALUES_TEST:' ) print ( ' Python version: %s' % ( platform.python_version ( ) ) ) print ( ' BETA_CDF_VALUES stores values of the BETA function.' ) print ( '' ) print ( ' A B X BETA_CDF(A,B,X)' ) print ( '' ) n_data = 0 while ( True ): n_data, a, b, x, f = beta_cdf_values ( n_data ) if ( n_data == 0 ): break print ( ' %12f %12f %12f %24.16g' % ( a, b, x, f ) ) # # Terminate. # print ( '' ) print ( 'BETA_CDF_VALUES_TEST:' ) print ( ' Normal end of execution.' ) return if ( __name__ == '__main__' ): from timestamp import timestamp timestamp ( ) beta_cdf_values_test ( ) timestamp ( )