function [ n_data, a, b, x, fx ] = 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: % % 28 April 2013 % % 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 FX, the value of the function. % n_max = 45; a_vec = [ ... 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 = [ ... 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 ]; fx_vec = [ ... 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, ... 0.918885, ... 0.21053, ... 0.182413 ]; x_vec = [ ... 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; end n_data = n_data + 1; if ( n_max < n_data ) n_data = 0; a = 0.0; b = 0.0; x = 0.0; fx = 0.0; else a = a_vec(n_data); b = b_vec(n_data); x = x_vec(n_data); fx = fx_vec(n_data); end return end