Wed Oct 8 08:47:43 2025 prob_test(): python version: 3.10.12 numpy version: 1.26.4 Test prob(). angle_cdf_test(): angle_cdf() evaluates the Angle CDF PDF parameter N = 5 PDF argument X = 0.5 CDF value = 0.0107809 angle_mean_test(): angle_mean() computes the Angle mean PDF parameter N = 5 PDF mean = 1.5708 angle_pdf_test(): angle_pdf() evaluates the Angle PDF 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 0.300408 0.983013 0.782658 0.300408 0.0312533 0.749896 0.531233 0.0312533 -0.206236 0.364342 0.299562 -0.206236 0.333913 0.993096 0.80964 0.333913 0.0404323 0.761914 0.540388 0.0404323 -0.268904 0.245068 0.243873 -0.268904 -0.531708 -0.274451 0.0629896 -0.531708 -0.242394 0.296102 0.266989 -0.242394 0.0551479 0.780643 0.555036 0.0551479 -0.237832 0.304805 0.271035 -0.237832 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 = -0.00633607 Sample variance = 0.117839 Sample maximum = 0.776374 Sample minimum = -0.776247 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 -0.746659 0.478513 0.231657 -0.746659 0.993915 2.88987 0.964868 0.993915 0.186306 0.323982 0.559652 0.186306 0.260776 0.329718 0.583978 0.260776 -0.347509 0.339467 0.387028 -0.347509 -0.999065 7.36405 0.0137632 -0.999065 0.859629 0.623015 0.829306 0.859629 0.073305 0.319169 0.523354 0.0733045 -0.974815 1.42729 0.0715903 -0.974815 0.395457 0.34656 0.629414 0.395457 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 = -0.0344268 Sample variance = 0.490467 Sample maximum = 0.999992 Sample minimum = -0.999997 PDF parameter A = 16 PDF mean = 0 PDF variance = 128 Sample size = 1000 Sample mean = 0.164069 Sample variance = 130.89 Sample maximum = 15.9994 Sample minimum = -15.999 benford_cdf_test(): benford_cdf() evaluates the Benford CDF. N CDF(N) CDF(N) by summing 1 0.30103 0.30103 2 0.477121 0.477121 3 0.60206 0.60206 4 0.69897 0.69897 5 0.778151 0.778151 6 0.845098 0.845098 7 0.90309 0.90309 8 0.954243 0.954243 9 1 1 N CDF(N) CDF(N) by summing 10 0.0413927 0.0413927 11 0.0791812 0.0791812 12 0.113943 0.113943 13 0.146128 0.146128 14 0.176091 0.176091 15 0.20412 0.20412 16 0.230449 0.230449 17 0.255273 0.255273 18 0.278754 0.278754 19 0.30103 0.30103 20 0.322219 0.322219 21 0.342423 0.342423 22 0.361728 0.361728 23 0.380211 0.380211 24 0.39794 0.39794 25 0.414973 0.414973 26 0.431364 0.431364 27 0.447158 0.447158 28 0.462398 0.462398 29 0.477121 0.477121 30 0.491362 0.491362 31 0.50515 0.50515 32 0.518514 0.518514 33 0.531479 0.531479 34 0.544068 0.544068 35 0.556303 0.556303 36 0.568202 0.568202 37 0.579784 0.579784 38 0.591065 0.591065 39 0.60206 0.60206 40 0.612784 0.612784 41 0.623249 0.623249 42 0.633468 0.633468 43 0.643453 0.643453 44 0.653213 0.653213 45 0.662758 0.662758 46 0.672098 0.672098 47 0.681241 0.681241 48 0.690196 0.690196 49 0.69897 0.69897 50 0.70757 0.70757 51 0.716003 0.716003 52 0.724276 0.724276 53 0.732394 0.732394 54 0.740363 0.740363 55 0.748188 0.748188 56 0.755875 0.755875 57 0.763428 0.763428 58 0.770852 0.770852 59 0.778151 0.778151 60 0.78533 0.78533 61 0.792392 0.792392 62 0.799341 0.799341 63 0.80618 0.80618 64 0.812913 0.812913 65 0.819544 0.819544 66 0.826075 0.826075 67 0.832509 0.832509 68 0.838849 0.838849 69 0.845098 0.845098 70 0.851258 0.851258 71 0.857332 0.857332 72 0.863323 0.863323 73 0.869232 0.869232 74 0.875061 0.875061 75 0.880814 0.880814 76 0.886491 0.886491 77 0.892095 0.892095 78 0.897627 0.897627 79 0.90309 0.90309 80 0.908485 0.908485 81 0.913814 0.913814 82 0.919078 0.919078 83 0.924279 0.924279 84 0.929419 0.929419 85 0.934498 0.934498 86 0.939519 0.939519 87 0.944483 0.944483 88 0.94939 0.94939 89 0.954243 0.954243 90 0.959041 0.959041 91 0.963788 0.963788 92 0.968483 0.968483 93 0.973128 0.973128 94 0.977724 0.977724 95 0.982271 0.982271 96 0.986772 0.986772 97 0.991226 0.991226 98 0.995635 0.995635 99 1 1 X PDF CDF CDF_INV 1 0.30103 0.30103 1 1 0.30103 0.30103 1 3 0.124939 0.60206 3 1 0.30103 0.30103 1 4 0.09691 0.69897 4 6 0.0669468 0.845098 6 3 0.124939 0.60206 3 1 0.30103 0.30103 1 3 0.124939 0.60206 3 1 0.30103 0.30103 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 benford_sample_test(): benford_mean() computes the mean; benford_sample() samples the distribution; benford_variance() computes the variance. PDF mean = 3.440236967123206 PDF variance = 6.056512631375667 Sample size = 10000 Sample mean = 3.4418 Sample variance = 6.161012759999998 Sample maximum = 9.0 Sample minimum = 1.0 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 1 0.75 1 1 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 1 0.75 1 1 0 0.25 0.25 0 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 = 0.735 Sample variance = 0.194775 Sample maximum = 1 Sample minimum = 0 bessel_i0_test(): bessel_i0() evaluates the Bessel function I0(X) X Exact F I0(X) 0 1 1 0.2 1.010025027795146 1.010025027795146 0.4 1.040401782229341 1.040401782229341 0.6 1.09204536431734 1.092045364317339 0.8 1.166514922869803 1.166514922869803 1 1.266065877752008 1.266065877752008 1.2 1.393725584134064 1.393725584134064 1.4 1.553395099731217 1.553395099731216 1.6 1.749980639738909 1.749980639738909 1.8 1.989559356618051 1.989559356618051 2 2.279585302336067 2.279585302336067 2.5 3.289839144050123 3.289839144050123 3 4.880792585865024 4.880792585865024 3.5 7.37820343222548 7.37820343222548 4 11.30192195213633 11.30192195213633 4.5 17.48117185560928 17.48117185560928 5 27.23987182360445 27.23987182360445 6 67.23440697647798 67.23440697647796 8 427.5641157218048 427.5641157218047 10 2815.716628466254 2815.716628466254 bessel_i0_values_test(): bessel_i0_values() stores values of the Bessel I function. of order 0. X I(0,X) 0.000000 1 0.200000 1.010025027795146 0.400000 1.040401782229341 0.600000 1.09204536431734 0.800000 1.166514922869803 1.000000 1.266065877752008 1.200000 1.393725584134064 1.400000 1.553395099731217 1.600000 1.749980639738909 1.800000 1.989559356618051 2.000000 2.279585302336067 2.500000 3.289839144050123 3.000000 4.880792585865024 3.500000 7.37820343222548 4.000000 11.30192195213633 4.500000 17.48117185560928 5.000000 27.23987182360445 6.000000 67.23440697647798 8.000000 427.5641157218048 10.000000 2815.716628466254 bessel_i1_test(): bessel_i1() evaluates the Bessel function I1(X) X Exact F I1(X) 0.000000 0 0 0.200000 0.1005008340281251 0.1005008340281251 0.400000 0.2040267557335706 0.2040267557335706 0.600000 0.3137040256049221 0.3137040256049221 0.800000 0.4328648026206398 0.4328648026206398 1.000000 0.565159103992485 0.5651591039924849 1.200000 0.7146779415526431 0.7146779415526432 1.400000 0.8860919814143274 0.8860919814143273 1.600000 1.08481063512988 1.08481063512988 1.800000 1.317167230391899 1.317167230391899 2.000000 1.590636854637329 1.590636854637329 2.500000 2.516716245288698 2.516716245288698 3.000000 3.953370217402609 3.953370217402608 3.500000 6.205834922258365 6.205834922258364 4.000000 9.759465153704451 9.759465153704447 4.500000 15.38922275373592 15.38922275373592 5.000000 24.33564214245053 24.33564214245052 6.000000 61.34193677764024 61.34193677764024 8.000000 399.8731367825601 399.8731367825602 10.000000 2670.988303701255 2670.988303701254 bessel_i1_values_test(): bessel_i1_values() stores values of the Bessel I function. of order 1. X I(1,X) 0.000000 0 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.000000 0.565159103992485 1.200000 0.7146779415526431 1.400000 0.8860919814143274 1.600000 1.08481063512988 1.800000 1.317167230391899 2.000000 1.590636854637329 2.500000 2.516716245288698 3.000000 3.953370217402609 3.500000 6.205834922258365 4.000000 9.759465153704451 4.500000 15.38922275373592 5.000000 24.33564214245053 6.000000 61.34193677764024 8.000000 399.8731367825601 10.000000 2670.988303701255 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 2 0.257143 0.757143 2 0 0.214286 0.214286 0 3 0.171429 0.928571 3 1 0.285714 0.5 1 3 0.171429 0.928571 3 2 0.257143 0.757143 2 2 0.257143 0.757143 2 1 0.285714 0.5 1 1 0.285714 0.5 1 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 = 1.584 Sample variance = 1.43494 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 0.632359 1.73958 0.904374 0.632359 12 12 0.524998 3.76328 0.595821 0.524998 12 12 0.461379 3.62189 0.353812 0.461379 12 12 0.61045 2.23116 0.860916 0.61045 12 12 0.463547 3.64807 0.361695 0.463547 12 12 0.460623 3.61245 0.351077 0.460623 12 12 0.529162 3.72602 0.611415 0.529162 12 12 0.458466 3.58463 0.343316 0.458466 12 12 0.596692 2.54355 0.828067 0.596692 12 12 0.349356 1.35803 0.0673621 0.349356 beta_cdf_values_test(): beta_cdf_values() stores values of the Beta function. A B X beta_cdf(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_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_inc_values_test(): beta_inc_values() stores values of the BETA function. A B X beta_inc(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_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 = 0.397803 Sample variance = 0.0388375 Sample maximum = 0.920984 Sample minimum = 0.0110819 beta_values_test(): beta_values() stores values of the Beta function. X Y BETA(X,Y) 0.200000 1.000000 5 0.400000 1.000000 2.5 0.600000 1.000000 1.666666666666667 0.800000 1.000000 1.25 1.000000 0.200000 5 1.000000 0.400000 2.5 1.000000 1.000000 1 2.000000 2.000000 0.1666666666666667 3.000000 3.000000 0.03333333333333333 4.000000 4.000000 0.007142857142857143 5.000000 5.000000 0.001587301587301587 6.000000 2.000000 0.02380952380952381 6.000000 3.000000 0.005952380952380952 6.000000 4.000000 0.001984126984126984 6.000000 5.000000 0.0007936507936507937 6.000000 6.000000 0.0003607503607503608 7.000000 7.000000 8.325008325008325e-05 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 0 0.00525219 0.00525219 0 2 0.181147 0.235169 2 4 0.312386 0.883971 4 4 0.312386 0.883971 4 4 0.312386 0.883971 4 4 0.312386 0.883971 4 5 0.116029 1 5 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 = 1.49 Sample variance = 1.0159 Sample maximum = 4 Sample minimum = 0 birthday_cdf_test(): birthday_cdf() evaluates the Birthday CDF birthday_cdf_inv() inverts the Birthday CDF. birthday_pdf() evaluates the Birthday PDF N PDF CDF CDF_inv 1 0 0 1 2 0.00273973 0.00273973 2 3 0.00546444 0.00820417 3 4 0.00815175 0.0163559 4 5 0.0107797 0.0271356 5 6 0.0133269 0.0404625 6 7 0.0157732 0.0562357 7 8 0.0180996 0.0743353 8 9 0.0202885 0.0946238 9 10 0.0223243 0.116948 10 11 0.0241932 0.141141 11 12 0.0258834 0.167025 12 13 0.0273855 0.19441 13 14 0.0286922 0.223103 14 15 0.0297988 0.252901 15 16 0.0307027 0.283604 16 17 0.0314037 0.315008 17 18 0.0319038 0.346911 18 19 0.0322071 0.379119 19 20 0.0323199 0.411438 20 21 0.03225 0.443688 21 22 0.032007 0.475695 22 23 0.0316019 0.507297 23 24 0.031047 0.538344 24 25 0.0303554 0.5687 25 26 0.0295411 0.598241 26 27 0.0286185 0.626859 27 28 0.0276022 0.654461 28 29 0.0265071 0.680969 29 30 0.0253477 0.706316 30 birthday_sample_test(): birthday_sample() samples the Birthday distribution. N Mean PDF 10 0.024 0.0223243 11 0.029 0.0241932 12 0.032 0.0258834 13 0.025 0.0273855 14 0.031 0.0286922 15 0.031 0.0297988 16 0.027 0.0307027 17 0.03 0.0314037 18 0.041 0.0319038 19 0.035 0.0322071 20 0.025 0.0323199 21 0.03 0.03225 22 0.038 0.032007 23 0.03 0.0316019 24 0.033 0.031047 25 0.029 0.0303554 26 0.034 0.0295411 27 0.028 0.0286185 28 0.032 0.0276022 29 0.03 0.0265071 30 0.025 0.0253477 31 0.02 0.0241384 32 0.023 0.0228929 33 0.015 0.0216243 34 0.028 0.020345 35 0.015 0.0190664 36 0.021 0.0177989 37 0.016 0.0165519 38 0.009 0.0153338 39 0.009 0.0141518 40 0.009 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 1.05609 1.85234 0.112189 1.05609 1.03002 1.98527 0.062195 1.03002 1.38674 1.00177 0.555587 1.38674 1.03633 1.95135 0.0746286 1.03633 1.21092 1.3254 0.353652 1.21092 1.13357 1.54496 0.24308 1.13357 1.46463 0.903991 0.629674 1.46463 1.38113 1.00964 0.549944 1.38113 1.18866 1.38192 0.323529 1.18866 1.27007 1.19547 0.428073 1.27007 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 = 1.38124 Sample variance = 0.0760889 Sample maximum = 1.99695 Sample minimum = 1.00045 buffon_box_pdf_test(): 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 9 3.33333 0.191741 100 98 3.06122 0.0803682 10000 9524 3.14994 0.00834435 1000000 954798 3.14203 0.000433199 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-Laplace needle dropping experiment. On a grid of cells of width A, a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1 Needle length L = 1 Trials Hits Est(Pi) Err 10 5 4 0.858407 100 70 2.85714 0.28445 10000 6360 3.14465 0.00306143 1000000 636468 3.14234 0.000749145 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 2.33157 0.612149 0.40382 2.33157 2.42367 0.603391 0.459896 2.42367 2.58913 0.559353 0.556524 2.58913 2.11254 0.576456 0.272142 2.11254 2.29226 0.611797 0.379752 2.29226 2.46725 0.594971 0.486013 2.46725 2.71446 0.509108 0.623588 2.71446 2.32216 0.612297 0.398058 2.32216 2.79868 0.47075 0.66487 2.79868 1.27081 0.0545977 0.00494699 1.27081 burr_sample_test(): burr_mean() computes the Burr mean burr_variance() computes the Burr variance burr_sample() samples the Burr distribution PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF parameter D = 2 PDF mean = 2.61227 PDF variance = 0.62513 Sample size = 1000 Sample mean = 2.575128 Sample variance = 0.577759 Sample maximum = 8.848001 Sample minimum = 1.141316 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 -0.73247 0.218323 0.33021 -0.73247 -1.11035 0.194515 0.251993 -1.11035 -1.41085 0.171829 0.196895 -1.41084 -1.33655 0.177626 0.209877 -1.33655 -1.19601 0.188286 0.235595 -1.19601 -1.2403 0.184978 0.227328 -1.2403 2.38888 0.101076 0.934603 2.38888 0.958564 0.204888 0.717684 0.958564 -0.289728 0.235416 0.431154 -0.289728 -0.344546 0.234056 0.418285 -0.344545 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 = -0.0437557 Sample variance = 2.1463 Sample maximum = 3.13878 Sample minimum = -3.1387 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 -15.6761 0.00297075 0.0535139 -15.6761 -3.11462 0.02716 0.168855 -3.11462 6.36207 0.034071 0.808233 6.36207 4.22769 0.068392 0.703312 4.22769 8.08344 0.0207556 0.854167 8.08344 -2.56469 0.0320055 0.185076 -2.56469 45.9904 0.000491179 0.978326 45.9904 -3.24011 0.026192 0.165508 -3.24011 1.81939 0.10572 0.48086 1.81939 2.94749 0.0964795 0.597376 2.94749 cauchy_sample_test(): cauchy_sample() samples the Cauchy distribution. PDF parameter A = 2 PDF parameter B = 3 PDF mean = Infinite PDF variance = Infinite Sample size = 1000 Sample mean = 3.52736 Sample variance = 2062.71 Sample maximum = 1062.55 Sample minimum = -210.996 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 0.879605 0.669133 0.842193 0.879605 -0.32739 0.336875 0.393831 -0.32739 0.817208 0.552293 0.804479 0.817208 -0.501762 0.367986 0.332685 -0.501762 -0.369777 0.342593 0.379434 -0.369777 0.421639 0.35104 0.638545 0.421639 0.043538 0.318612 0.513863 0.043538 0.672392 0.430035 0.734733 0.672392 0.993832 2.87032 0.964628 0.993832 0.43723 0.353933 0.64404 0.43723 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 = 0.030192 Sample variance = 0.499302 Sample maximum = 1 Sample minimum = -0.999997 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 4.6178 0.254218 0.648459 4.61816 6.89378 0.0450708 0.966201 6.89453 7.37526 0.0252008 0.982754 7.375 3.48063 0.284393 0.326558 3.48047 3.65106 0.291176 0.37567 3.65137 3.85956 0.293454 0.436731 3.85938 6.68477 0.0567427 0.955596 6.68359 4.5738 0.258082 0.637186 4.57373 5.19382 0.194656 0.778339 5.19336 7.45878 0.0226221 0.984749 7.46094 chi_sample_test(): chi_mean() computes the Chi mean chi_variance() computes the Chi variance chi_sample() samples the Chi distribution. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 4.19154 PDF variance = 1.81408 Sample size = 1000 Sample mean = 4.14307 Sample variance = 1.79411 Sample maximum = 8.43105 Sample minimum = 1.24145 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 4.86921 0.106675 0.300982 2.20006 0.522274 0.100561 0.971297 10.8167 1.90168 0.18371 0.753836 5.42764 2.10307 0.183704 0.716809 5.04027 6.13331 0.0714173 0.189411 1.59 1.05688 0.155764 0.901051 7.806 1.31039 0.170135 0.85961 6.91608 1.70621 0.18175 0.789589 5.85284 4.09986 0.131958 0.392659 2.71072 2.70389 0.174899 0.608535 4.10892 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 = 10.1277 Sample variance = 18.9669 Sample maximum = 26.3748 Sample minimum = 1.00674 chi_square_noncentral_sample_test(): chi_square_noncentral_mean() computes the Chi Square Noncentral mean. chi_square_noncentral_sample() samples the Chi Square Noncentral PDF. chi_square_noncentral_variance() computes the Chi Square Noncentral variance. PDF parameter A = 3 PDF parameter B = 2 PDF mean = 5 PDF variance = 14 Sample size = 1000 Sample mean = 4.89931 Sample variance = 13.0355 Sample maximum = 22.3114 Sample minimum = 0.140361 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 means = 1 5 PDF variances = 0.5625 0.5625 Sample size = 1000 Sample mean = 0.996956 5.00988 Sample variance = 0.548071 0.587639 Sample maximum = 3.05181 7.27011 Sample minimum = -1.49825 2.19935 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 means = 0 0 PDF variances = 1 1 Sample size = 1000 Sample mean = -0.00798695 -0.00442491 Sample variance = 0.918627 1.00123 Sample maximum = 3.13506 3.06898 Sample minimum = -2.99602 -3.10117 cosine_cdf_test(): cosine_cdf() evaluates the Cosine CDF. cosine_cdf_inv() inverts the Cosine CDF. cosine_pdf() evaluates the Cosine PDF. PDF parameter A = 2 PDF parameter B = 1 X PDF CDF CDf_inv 2.17871 0.15662 0.556734 2.17871 2.66805 0.124942 0.704913 2.66805 2.75395 0.116022 0.728941 2.75395 3.80243 -0.0365365 0.94177 3.80243 0.357107 -0.0114647 0.0797839 0.357107 2.05906 0.158877 0.518793 2.05906 -0.123029 -0.083491 0.026612 -0.123029 2.43757 0.14416 0.637081 2.43757 2.69911 0.121819 0.713689 2.69911 1.70778 0.152408 0.407642 1.70778 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 = 2.01611 Sample variance = 1.26792 Sample maximum = 4.77344 Sample minimum = -0.675262 coupon_sample_test(): coupon_sample() samples the coupon PDF. Number of coupon types is 5 Expected wait is about 8.04719 0 10 1 9 2 15 3 9 4 7 5 21 6 6 7 10 8 28 9 12 Average wait was 12.7 Number of coupon types is 10 Expected wait is about 23.0259 0 26 1 34 2 48 3 48 4 39 5 44 6 38 7 22 8 15 9 17 Average wait was 33.1 Number of coupon types is 15 Expected wait is about 40.6208 0 39 1 28 2 30 3 34 4 28 5 53 6 24 7 36 8 45 9 44 Average wait was 36.1 Number of coupon types is 20 Expected wait is about 59.9146 0 50 1 103 2 48 3 91 4 115 5 44 6 51 7 75 8 61 9 75 Average wait was 71.3 Number of coupon types is 25 Expected wait is about 80.4719 0 91 1 61 2 177 3 112 4 111 5 80 6 87 7 103 8 91 9 112 Average wait was 102.5 coupon_complete_pdf_test(): coupon_complete_pdf() evaluates the Coupon Complete PDF. Number of coupon types is 2 BOX_NUM PDF CDF 1 0 0 2 0.5 0.5 3 0.25 0.75 4 0.125 0.875 5 0.0625 0.9375 6 0.03125 0.96875 7 0.015625 0.984375 8 0.0078125 0.992188 9 0.00390625 0.996094 10 0.00195312 0.998047 11 0.000976562 0.999023 12 0.000488281 0.999512 13 0.000244141 0.999756 14 0.00012207 0.999878 15 6.10352e-05 0.999939 16 3.05176e-05 0.999969 17 1.52588e-05 0.999985 18 7.62939e-06 0.999992 19 3.8147e-06 0.999996 20 1.90735e-06 0.999998 Number of coupon types is 3 BOX_NUM PDF CDF 1 0 0 2 0 0 3 0.222222 0.222222 4 0.222222 0.444444 5 0.17284 0.617284 6 0.123457 0.740741 7 0.085048 0.825789 8 0.0576132 0.883402 9 0.0387136 0.922116 10 0.0259107 0.948026 11 0.0173077 0.965334 12 0.0115497 0.976884 13 0.00770358 0.984587 14 0.00513698 0.989724 15 0.00342507 0.993149 16 0.00228352 0.995433 17 0.00152239 0.996955 18 0.00101494 0.99797 19 0.000676634 0.998647 20 0.000451091 0.999098 Number of coupon types is 4 BOX_NUM PDF CDF 1 0 0 2 0 0 3 0 0 4 0.09375 0.09375 5 0.140625 0.234375 6 0.146484 0.380859 7 0.131836 0.512695 8 0.110229 0.622925 9 0.0884399 0.711365 10 0.0692368 0.780602 11 0.0533867 0.833988 12 0.040771 0.874759 13 0.0309441 0.905703 14 0.0233911 0.929094 15 0.0176349 0.946729 16 0.0132719 0.960001 17 0.00997682 0.969978 18 0.00749406 0.977472 19 0.00562627 0.983098 20 0.00422256 0.987321 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_variance() computes the Deranged variance. deranged_sample() samples the Deranged distribution. PDF parameter A = 7 PDF mean = 1 PDF variance = 1 Sample size = 1000 Sample mean = 1.031 Sample variance = 1.06004 Sample maximum = 5 Sample minimum = 0 digamma_test(): digamma() computes the Digamma or Psi function. Compare the result to tabulated values. X FX FX2 (Tabulated) (DIGAMMA) DIFF 0.1 -10.42375494041108 -10.42375494041114 5.862e-14 0.2 -5.289039896592188 -5.289039896592243 5.507e-14 0.3 -3.502524222200133 -3.502524222200181 4.796e-14 0.4 -2.561384544585116 -2.561384544585158 4.174e-14 0.5 -1.963510026021423 -1.963510026021564 1.406e-13 0.6 -1.54061921389319 -1.540619213893313 1.232e-13 0.7 -1.220023553697935 -1.220023553698041 1.064e-13 0.8 -0.9650085667061385 -0.9650085667062314 9.281e-14 0.9 -0.7549269499470515 -0.7549269499471327 8.127e-14 1 -0.5772156649015329 -0.5772156649016036 7.072e-14 1.1 -0.4237549404110768 -0.4237549404111393 6.251e-14 1.2 -0.2890398965921883 -0.2890398965922431 5.479e-14 1.3 -0.1691908888667997 -0.1691908888668481 4.841e-14 1.4 -0.06138454458511615 -0.06138454458515841 4.226e-14 1.5 0.03648997397857652 0.03648997397843547 1.411e-13 1.6 0.1260474527734763 0.1260474527733536 1.227e-13 1.7 0.208547874873494 0.2085478748733869 1.071e-13 1.8 0.2849914332938615 0.2849914332937686 9.293e-14 1.9 0.3561841611640597 0.3561841611639783 8.143e-14 2 0.4227843350984671 0.4227843350983961 7.094e-14 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 7.23529 0.00175292 0.999452 6.875 -0.638639 0.517541 0.174696 -0.638672 0.0691575 0.636586 0.543887 0.0690918 -0.869331 0.38353 0.114607 -0.869141 -0.511663 0.57454 0.220385 -0.511719 -0.709965 0.478949 0.153227 -0.709961 0.321342 0.623759 0.691682 0.321289 0.114225 0.636374 0.572093 0.114258 -0.405744 0.607488 0.266412 -0.405762 -0.379148 0.613535 0.279126 -0.37915 PDF parameter A = 0.785398 PDF parameter B = 0.5 X PDF CDF CDf_inv 1.31882 0.12971 0.764442 1.31885 -0.121129 0.318199 0.383204 -0.121094 1.64056 0.0835643 0.804197 1.63965 -0.0169418 0.31831 0.415053 -0.0170898 2.2174 0.0441026 0.851693 2.21777 1.09955 0.17311 0.729057 1.09912 1.07714 0.178007 0.724979 1.07715 -0.85925 0.227879 0.228272 -0.859375 0.715786 0.2598 0.645129 0.71582 2.56675 0.0354732 0.871259 2.56689 PDF parameter A = 1.5708 PDF parameter B = 0 X PDF CDF CDf_inv -0.712936 0.211042 0.302853 -0.712891 1.26023 0.122986 0.786488 1.26025 1.95502 0.0660105 0.849501 1.95605 0.31161 0.290137 0.596153 0.311523 8.48266 0.00436306 0.962648 8.49609 -0.724812 0.20868 0.300361 -0.724609 -3.61104 0.0226723 0.0859941 -3.60938 -0.564133 0.241465 0.336507 -0.564453 -1.61081 0.0885499 0.176846 -1.61035 2.00537 0.0633895 0.852757 2.00537 dipole_sample_test(): dipole_sample() samples the Dipole distribution. PDF parameter A = 0 PDF parameter B = 1 Sample size = 1000 Sample mean = -0.0243116 Sample variance = 0.705598 Sample maximum = 3.78878 Sample minimum = -6.67586 PDF parameter A = 0.785398 PDF parameter B = 0.5 Sample size = 1000 Sample mean = 0.735554 Sample variance = 175.775 Sample maximum = 220.298 Sample minimum = -192.406 PDF parameter A = 1.5708 PDF parameter B = 0 Sample size = 1000 Sample mean = 1.29569 Sample variance = 17467 Sample maximum = 3344.23 Sample minimum = -2413.68 dirichlet_pdf_test(): dirichlet_pdf() evaluates the Dirichlet PDF. Number of components N = 3 PDF parameters A: 0: 0.25 1: 0.5 2: 1.25 PDF arguments X: 0: 0.5 1: 0.125 2: 0.375 PDF value = 0.63907 dirichlet_sample_test(): dirichlet_sample() samples the Dirichlet distribution dirichlet_mean() computes the Dirichlet mean dirichlet_variance() computes the Dirichlet variance. Number of components N = 3 PDF parameters A: 0: 0.25 1: 0.5 2: 1.25 PDF mean, variance: 0 0.125 0.0364583 1 0.25 0.0625 2 0.625 0.078125 Second moment matrix: Col: 0 1 2 Row 0 : 0.0520833 0.0208333 0.0520833 1 : 0.0208333 0.125 0.104167 2 : 0.0520833 0.104167 0.46875 Sample size = 1000 Observed Min, Max, Mean, Variance: 0 1.52198e-19 0.923977 0.124396 0.0348029 1 3.41118e-08 0.992167 0.247284 0.0616088 2 0.00143661 1 0.62832 0.0762035 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 value = 2.12288 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 Observed Min, Max, Mean, Variance: 0 1.83611e-11 0.951501 0.30909 0.0598015 1 2.02309e-07 0.993302 0.161615 0.0376538 2 0.00618205 0.997771 0.529295 0.0608868 discrete_cdf_test(): discrete_cdf() evaluates the Discrete CDF discrete_cdf_inv() inverts the Discrete CDF. discrete_pdf() evaluates the Discrete PDF PDF parameter A = 6 PDF parameters B: 0: 1 1: 2 2: 6 3: 2 4: 4 5: 1 X PDF CDF CDf_inv 2 0.125 0.1875 2 1 0.0625 0.0625 1 3 0.375 0.5625 3 4 0.125 0.6875 4 5 0.25 0.9375 5 4 0.125 0.6875 4 2 0.125 0.1875 2 3 0.375 0.5625 3 5 0.25 0.9375 5 5 0.25 0.9375 5 discrete_sample_test(): discrete_mean() computes the Discrete mean discrete_sample() samples the Discrete distribution discrete_variance() computes the Discrete variance. PDF parameter A = 6 PDF parameters B: 0: 1 1: 2 2: 6 3: 2 4: 4 5: 1 PDF mean = 3.5625 PDF variance = 1.74609 Sample size = 1000 Sample mean = 3.572 Sample variance = 1.73682 Sample maximum = 6 Sample minimum = 1 disk_sample_test(): disk_mean() returns the Disk mean. disk_sample() samples the Disk distribution. disk_variance() returns the Disk variance. X coordinate of center is A = 10 Y coordinate of center is B = 4 Radius is C = 5 Disk mean = 10 4 Disk variance = 12.5 Sample size = 1000 Sample mean = 10.0151 4.07801 Sample variance = 12.6679 Sample maximum = 14.884 8.92267 Sample minimum = 5.01431 -0.898475 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 4.5 0.2 0.7 4.5 4.5 0.2 0.7 4.5 0 0.1 0.1 0 4.5 0.2 0.7 4.5 2 0.3 0.5 2 6 0.1 0.8 6 0 0.1 0.1 0 2 0.3 0.5 2 4.5 0.2 0.7 4.5 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 = 4.1175 Sample variance = 10.8089 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' 'i' 0.06966 0.46699 'i' 'b' 0.01492 0.09659 'b' 's' 0.06327 0.82649 's' 'n' 0.06749 0.60804 'n' 'i' 0.06966 0.46699 'i' 'r' 0.05987 0.76322 'r' 't' 0.09056 0.91705 't' 'n' 0.06749 0.60804 'n' 'i' 0.06966 0.46699 'i' 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 17 0.0344199 0.520808 17 3 0.0186633 0.0404739 3 31 0.0151552 0.856106 31 8 0.0355324 0.199242 8 6 0.0319642 0.128468 6 16 0.0354923 0.486388 16 22 0.0273033 0.674445 22 7 0.0352418 0.16371 7 6 0.0319642 0.128468 6 12 0.0379681 0.341262 12 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 = 19.983 Sample variance = 152.413 Sample maximum = 73 Sample minimum = 1 english_word_length_cdf_test(): english_word_length_cdf() evaluates the English Word Length CDF english_word_length_cdf_inv() inverts the English Word Length CDF. english_word_length_pdf() evaluates the English Word Length PDF X PDF CDF CDf_inv 4 0.156785 0.570067 4 3 0.211926 0.413282 3 3 0.211926 0.413282 3 8 0.0562317 0.897307 8 6 0.0852426 0.763833 6 7 0.0772423 0.841075 7 7 0.0772423 0.841075 7 12 0.00917028 0.99028 12 11 0.0158205 0.981109 11 3 0.211926 0.413282 3 english_word_length_sample_test(): english_word_length_mean() computes the English Word Length mean english_word_length_sample() samples the English Word Length distribution english_word_length_variance() computes the English Word Length variance. PDF mean = 4.73912 PDF variance = 7.05635 Sample size = 1000 Sample mean = 4.762 Sample variance = 6.56336 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 9.91807 0.0575291 0.821762 9.91797 3.03366 0.0935045 0.0834229 3.0332 5.974 0.128588 0.452848 5.97461 3.38229 0.107786 0.118598 3.38281 2.45647 0.0640051 0.0376665 2.45703 7.49209 0.102544 0.629623 7.49219 17.2752 0.00483976 0.987649 17.2812 2.36297 0.0587336 0.0319277 2.36328 4.82085 0.135056 0.299094 4.82031 4.28611 0.130519 0.227826 4.28613 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 = 7.05763 Sample variance = 12.267 Sample maximum = 23.8899 Sample minimum = 1.29679 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 1.36372 0.416859 0.166283 1.36372 7.8054 0.0166416 0.966717 7.8054 2.68406 0.215418 0.569164 2.68406 3.64941 0.132941 0.734119 3.64941 1.57501 0.375067 0.249866 1.57501 7.83361 0.0164085 0.967183 7.83361 2.73709 0.20978 0.580439 2.73709 2.0478 0.296104 0.407792 2.0478 2.26383 0.265787 0.468426 2.26383 2.77519 0.205823 0.588355 2.77519 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 = 10.7284 Sample variance = 89.4511 Sample maximum = 61.6419 Sample minimum = 1.00751 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 0.0410911 0.959742 0.0402583 0.0410911 0.508252 0.601546 0.398454 0.508252 2.4536 0.0859835 0.914017 2.4536 0.246532 0.781506 0.218494 0.246532 0.543982 0.580432 0.419568 0.543982 0.0961989 0.908283 0.0917167 0.0961989 0.669111 0.512164 0.487836 0.669111 1.02423 0.359073 0.640927 1.02423 2.2132 0.10935 0.89065 2.2132 0.59472 0.551717 0.448283 0.59472 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 = 0.951181 Sample variance = 0.771489 Sample maximum = 5.14349 Sample minimum = 0.00134078 extreme_values(): 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 10.5902 0.0179694 0.944524 10.5902 2.51089 0.120957 0.430239 2.51089 1.32028 0.119274 0.285276 1.32028 5.54662 0.0752139 0.735944 5.54662 4.93325 0.0860765 0.686495 4.93325 2.58459 0.120462 0.439136 2.58459 5.85881 0.0698657 0.758586 5.85881 0.644054 0.108821 0.207749 0.644054 7.56409 0.0446094 0.855131 7.56409 0.834035 0.112483 0.22878 0.834035 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 = 3.40594 Sample variance = 13.7497 Sample maximum = 28.9898 Sample minimum = -4.19672 f_cdf_test(): f_cdf() evaluates the F CDF. f_pdf() evaluates the F PDF. PDF parameter M = 1 PDF parameter N = 1 X M N PDF CDF 0.21271 1 1 0.569114 0.724896 0.267651 1 1 0.485362 0.696058 443.793 1 1 3.39706e-05 0.030197 0.392577 1 1 0.364812 0.643671 0.139909 1 1 0.746546 0.772133 4.20637 1 1 0.02981 0.288811 48.5069 1 1 0.000923173 0.0907863 0.224094 1 1 0.549314 0.718531 0.000504186 1 1 14.1689 0.985708 0.675417 1 1 0.231175 0.562059 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 = 1.46726 Sample variance = 3.07695 Sample maximum = 30.4101 Sample minimum = 0.086953 fermi_dirac_sample_test(): fermi_dirac_sample() samples the Fermi Dirac distribution. U = 1 V = 1 SAMPLE_NUM = 10000 Sample mean = 0.59357 Sample variance = 0.175657 Maximum value = 2.66628 Minimum value = 5.86047e-06 U = 2 V = 1 SAMPLE_NUM = 10000 Sample mean = 1.05977 Sample variance = 0.440937 Maximum value = 3.55307 Minimum value = 5.45518e-05 U = 4 V = 1 SAMPLE_NUM = 10000 Sample mean = 2.01568 Sample variance = 1.4301 Maximum value = 5.35829 Minimum value = 0.000439148 U = 8 V = 1 SAMPLE_NUM = 10000 Sample mean = 4.03099 Sample variance = 5.41793 Maximum value = 9.18763 Minimum value = 0.00121999 U = 16 V = 1 SAMPLE_NUM = 10000 Sample mean = 7.97947 Sample variance = 21.7776 Maximum value = 17.2049 Minimum value = 0.000490664 U = 32 V = 1 SAMPLE_NUM = 10000 Sample mean = 16.0416 Sample variance = 85.1306 Maximum value = 33.5292 Minimum value = 0.000768926 U = 1 V = 0.25 SAMPLE_NUM = 10000 Sample mean = 0.510559 Sample variance = 0.0900829 Maximum value = 1.42113 Minimum value = 0.000581608 fisher_pdf_test(): fisher_pdf() evaluates the Fisher PDF. PDF Input: Concentration parameter KAPPA = 0 1 0 0 X PDF 0.160862 -0.861956 0.480786 0.0795775 0.217045 -0.775125 0.593357 0.0795775 0.520916 -0.00352206 -0.853601 0.0795775 0.424474 -0.872972 -0.240296 0.0795775 -0.543594 -0.450488 0.708213 0.0795775 0.91479 0.35391 -0.194695 0.0795775 0.0492219 0.825937 0.56161 0.0795775 -0.620676 0.742895 0.250734 0.0795775 0.306943 0.377548 0.873638 0.0795775 -0.010777 0.967233 -0.253661 0.0795775 PDF Input: Concentration parameter KAPPA = 0.5 1 0 0 X PDF -0.815047 0.417793 -0.401432 0.0507993 0.997168 -0.0316728 -0.0682175 0.125712 0.185051 0.930313 -0.31666 0.083758 0.099562 0.927309 0.360811 0.0802532 -0.0449015 -0.267635 -0.962474 0.0746608 -0.192221 -0.699736 0.688055 0.069359 0.0653668 0.728473 -0.681948 0.0788928 0.692076 -0.654782 -0.303795 0.107926 0.522569 -0.0869489 0.848152 0.0991556 0.656912 -0.753967 0.00117033 0.106045 PDF Input: Concentration parameter KAPPA = 10 1 0 0 X PDF 0.948607 0.0129447 0.316192 0.95197 0.919371 0.144365 0.365944 0.710648 0.842999 0.537409 0.0233075 0.331112 0.899088 0.33837 -0.277754 0.580181 0.847011 0.0168887 0.531308 0.344664 0.928199 -0.259038 -0.267106 0.776235 0.959393 0.0650991 -0.274457 1.0604 0.905393 -0.275452 -0.323094 0.617941 0.657647 -0.0692154 0.75014 0.0518799 0.872904 0.487185 -0.0262643 0.446527 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 6.45363 0.0246406 0.952997 6.45363 2.1383 0.346396 0.155666 2.1383 2.87076 0.396908 0.450064 2.87076 2.67989 0.41724 0.372092 2.67989 3.77417 0.214418 0.727427 3.77417 5.23814 0.0609134 0.904903 5.23814 3.06409 0.362545 0.523637 3.06409 1.67945 0.160304 0.0377301 1.67945 3.01644 0.371886 0.506141 3.01644 3.15348 0.344025 0.555226 3.15348 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 = 3.32745 Sample variance = 2.54666 Sample maximum = 18.1803 Sample minimum = 1.05564 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 1.82541 0.191737 0.375666 1.82562 1.12745 0.204706 0.236989 1.12751 0.486594 0.211412 0.103376 0.486591 3.57666 0.139456 0.66888 3.57694 4.00868 0.12417 0.725836 4.0089 0.584613 0.210726 0.124065 0.584551 2.75192 0.166798 0.542354 2.75162 4.4937 0.106911 0.781869 4.49349 3.04345 0.15754 0.589645 3.04347 1.7463 0.193483 0.360428 1.74681 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 = 2.92031 Sample variance = 4.32146 Sample maximum = 13.6891 Sample minimum = 0.00391197 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 1.56009 0.389178 0.768464 1.56009 5.49834 0.00326275 0.994002 5.49834 1.54026 0.405407 0.760589 1.54026 1.67184 0.310027 0.807349 1.67184 1.1176 0.939412 0.488521 1.1176 0.874993 1.1503 0.224755 0.874993 0.809001 1.05948 0.151275 0.809001 1.09499 0.9743 0.466879 1.09499 1.0651 1.0189 0.43709 1.0651 0.774897 0.970016 0.116583 0.774897 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 = 1.33151 Sample variance = 0.749048 Sample maximum = 17.457 Sample minimum = 0.524884 gamma_cdf_test(): gamma_cdf() evaluates the Gamma CDF. gamma_pdf() evaluates the Gamma PDF. PDF parameter A = 1 PDF parameter B = 1.5 PDF parameter C = 3 X PDF CDF 2.22401 0.0981475 0.0497517 6.35947 0.119458 0.692441 3.9564 0.180409 0.315456 2.76222 0.142102 0.115097 4.22048 0.17952 0.363039 3.14199 0.16299 0.173307 4.07363 0.18034 0.336607 6.09961 0.128612 0.66021 4.28664 0.178904 0.374897 6.14632 0.126963 0.666178 gamma_sample_test(): gamma_mean() computes the Gamma mean gamma_sample() samples the Gamma distribution gamma_variance() computes the Gamma variance. TEST NUMBER: 0 PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 2 PDF mean = 7 PDF variance = 18 Sample size = 1000 Sample mean = 7.00176 Sample variance = 18.8093 Sample maximum = 31.3772 Sample minimum = 1.03982 TEST NUMBER: 1 PDF parameter A = 2 PDF parameter B = 0.5 PDF parameter C = 0.5 PDF mean = 2.25 PDF variance = 0.125 Sample size = 1000 Sample mean = 2.23439 Sample variance = 0.099981 Sample maximum = 4.5501 Sample minimum = 2 gamma_inc_values_test(): gamma_inc_values() stores values of the incomplete Gamma function. A X gamma_inc(A,X) 0.100000 0.030000 2.49030283630057 0.100000 0.300000 0.8718369702247978 0.100000 1.500000 0.1079213896175866 0.500000 0.075000 1.238121685818417 0.500000 0.750000 0.3911298052193973 0.500000 3.500000 0.01444722098952533 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.006737946999085467 1.100000 0.100000 0.8827966752611692 1.100000 1.000000 0.3908330082003269 1.100000 5.000000 0.008051456628620992 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.00729505572443613 6.000000 2.500000 114.9574754165633 6.000000 12.000000 2.440923530031405 11.000000 16.000000 280854.6620274718 26.000000 25.000000 8.576480283455533e+24 41.000000 45.000000 2.085031346403364e+47 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 2 0.1875 0.4375 3 2 0.1875 0.4375 3 2 0.1875 0.4375 3 8 0.033371 0.899887 9 2 0.1875 0.4375 3 1 0.25 0.25 2 9 0.0250282 0.924915 10 3 0.140625 0.578125 4 5 0.0791016 0.762695 6 1 0.25 0.25 2 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 = 3.939 Sample variance = 10.8253 Sample maximum = 23 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 0.0989366 2.36308 0.264514 0.0989366 0.15304 2.05512 0.383906 0.15304 0.252763 1.56056 0.563414 0.252763 0.523022 0.650467 0.849111 0.523022 0.199378 1.81371 0.473464 0.199378 0.0721799 2.5259 0.199123 0.0721799 0.00417603 2.97118 0.0124679 0.00417603 0.512551 0.67547 0.842169 0.512551 0.54646 0.597091 0.863724 0.54646 0.334887 1.22128 0.677237 0.334887 gompertz_sample_test(): gompertz_sample() samples the Gompertz distribution PDF parameter A = 2 PDF parameter B = 3 Sample size = 1000 Sample mean = 0.275864 Sample variance = 0.0551415 Sample maximum = 1.42771 Sample minimum = 0.00021732 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 0.224641 0.359355 0.449867 0.224641 5.04958 0.00637106 0.993608 5.04958 0.195848 0.361322 0.439491 0.195848 -0.367882 0.340688 0.235824 -0.367882 2.063 0.111909 0.88067 2.063 2.03038 0.115133 0.876968 2.03038 0.506017 0.329919 0.547227 0.506017 -0.835599 0.229788 0.0996397 -0.835599 -0.0818304 0.366616 0.33781 -0.0818304 -0.422681 0.331752 0.217393 -0.422681 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 = 0.600834 Sample variance = 1.51392 Sample maximum = 9.48093 Sample minimum = -1.94958 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 0.55117 0.384077 0.217133 0.55117 1.61657 0.287768 0.581074 1.61657 3.30449 0.101886 0.901516 3.30449 0.0356965 0.398879 0.0142401 0.0356965 0.367954 0.392247 0.145968 0.367954 0.829959 0.366029 0.321843 0.829959 0.0945618 0.398497 0.0377106 0.0945618 1.88816 0.255487 0.654872 1.88816 1.42737 0.309248 0.524577 1.42737 1.73734 0.27356 0.614973 1.73734 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 = 8.12141 Sample variance = 35.7141 Sample maximum = 32.7849 Sample minimum = 0.0198487 hypergeometric_cdf_test(): hypergeometric_cdf() evaluates the Hypergeometric CDF. hypergeometric_pdf() evaluates the Hypergeometric PDF. PDF argument X = 7 Total number of balls = 100 Number of white balls = 7 Number of balls taken = 10 PDF value = = 7.49646e-09 CDF value = = 1 hypergeometric_sample_test(): hypergeometric_mean() computes the Hypergeometric mean hypergeometric_sample() samples the Hypergeometric distribution hypergeometric_variance() computes the Hypergeometric variance. PDF parameter N = 10 PDF parameter M = 7 PDF parameter L = 100 PDF mean = 0.7 PDF variance = 0.591818 Sample size = 1000 Sample mean = 0.663 Sample variance = 0.557431 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_factorial_log_test(): i4_factorial_log() evaluates log(N!). N lfact elfact fact 0 0 1 1 1 0 1 1 2 0.693147 2 2 3 1.79176 6 6 4 3.17805 24 24 5 4.78749 120 120 6 6.57925 720 720 7 8.52516 5040 5040 8 10.6046 40320 40320 9 12.8018 362880 362880 10 15.1044 3.6288e+06 3628800 11 17.5023 3.99168e+07 39916800 12 19.9872 4.79002e+08 479001600 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 False 98 False 99 False 100 True 101 False 102 False 103 False i4mat_print_test(): i4mat_print() prints an I4MAT. A 5 x 6 integer matrix: Col: 0 1 2 3 4 5 Row 0: 11 12 13 14 15 16 1: 21 22 23 24 25 26 2: 31 32 33 34 35 36 3: 41 42 43 44 45 46 4: 51 52 53 54 55 56 i4mat_print_some_test(): i4mat_print_some() prints some of an I4MAT. Here is I4MAT, rows 0:2, cols 3:5: Col: 3 4 5 Row 0: 14 15 16 1: 24 25 26 2: 34 35 36 i4row_max_test(): i4row_max() computes maximums of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 Row maximums: 0 4 1 8 2 12 i4row_mean_test(): i4row_mean() computes row means of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 The row means: 0: 2.5 1: 6.5 2: 10.5 i4row_min_test(): i4row_min() computes minimums of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 Row minimums: 0 1 1 5 2 9 i4row_variance_test(): i4row_variance() computes variances of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 The row variances: 0: 1.66667 1: 1.66667 2: 1.66667 i4vec_print_test(): i4vec_print() prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 i4vec_run_count_test(): i4vec_run_count() counts runs in an I4VEC Run Count Sequence 8 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 1 1 10 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 16 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 0 10 1 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 15 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0 1 7 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 10 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 0 11 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 12 1 0 0 1 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 0 6 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 i4vec_unique_count_test(): i4vec_unique_count() counts unique entries in an I4VEC. Input vector: 0 3 1 5 2 6 3 5 4 15 5 5 6 8 7 10 8 17 9 1 10 8 11 17 12 3 13 12 14 11 15 20 16 12 17 19 18 6 19 18 Number of unique entries is 13 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 0.403345 0.27095 0.038249 1.70697 0.196212 0.400986 13.4331 0.00927245 0.914754 14.5201 0.00794403 0.924086 0.572915 0.33114 0.0905362 34.8775 0.000983984 0.986258 1.74373 0.192119 0.408123 4.22113 0.0646823 0.684624 0.531956 0.324099 0.0771047 1.35007 0.242367 0.323075 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 = 1.94351 Sample variance = 2.23222 Sample maximum = 13.69 Sample minimum = 0.179744 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 -1.29697 0.0792791 0.158558 -1.29697 1.16887 0.229758 0.540484 1.16887 0.263385 0.172976 0.345952 0.263385 -2.37968 0.0461373 0.0922745 -2.37968 3.64323 0.0666761 0.866648 3.64323 -2.25087 0.0492064 0.0984128 -2.25087 -15.2636 7.35104e-05 0.000147021 -15.2636 3.27678 0.0800834 0.839833 3.27678 1.8143 0.166386 0.667227 1.8143 -1.70932 0.0645087 0.129017 -1.70932 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 = 1.0373 Sample variance = 8.10072 Sample maximum = 13.5712 Sample minimum = -13.4029 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 2.10552 0.196442 0.178615 2.10552 2.70439 0.141014 0.278696 2.70439 4.4883 0.0650136 0.448933 4.4883 3.94703 0.0794296 0.410052 3.94703 4.72288 0.0600413 0.463588 4.72288 3.15073 0.112362 0.334884 3.15073 2.06652 0.200569 0.170875 2.06652 3.2693 0.106221 0.347838 3.2693 9.99494 0.0187131 0.637257 9.99494 2.05481 0.201807 0.168518 2.05481 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 27715.7 6.36411e-06 0.540666 27715.7 129966 9.99432e-07 0.784915 129966 149236 8.27628e-07 0.802435 149236 652972 8.73184e-08 0.934011 652972 17127.8 1.02875e-05 0.455493 17127.8 104637 1.33319e-06 0.755706 104637 57241 2.83073e-06 0.664383 57241 1806.23 5.29245e-05 0.133164 1806.23 7168.38 2.18401e-05 0.308919 7168.38 7532.08 2.10098e-05 0.316709 7532.08 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 = 18.0673 Sample variance = 6977.9 Sample maximum = 2058.65 Sample minimum = 0.00245999 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 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 log_series_sample_test(): log_series_mean() computes the Log Series mean log_series_variance() computes the Log Series variance log_series_sample() samples the Log Series distribution. PDF parameter A = 0.25 PDF mean = 1.15869 PDF variance = 0.202361 Sample size = 1000 Sample mean = 1.144 Sample variance = 0.183264 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 7.35094 0.0590801 0.565313 7.35094 5.29712 0.0819869 0.42301 5.29712 6.07523 0.0714861 0.482532 6.07523 3.75855 0.115548 0.27399 3.75855 14.904 0.0291395 0.872272 14.904 3.76887 0.115232 0.275181 3.76887 9.89711 0.0438809 0.694478 9.89711 4.80691 0.0903479 0.380836 4.80691 2.18454 0.198804 0.038329 2.18454 9.70754 0.0447379 0.686079 9.70754 log_uniform_sample_test(): log_uniform_mean() computes the Log Uniform mean log_uniform_sample() samples the Log Uniform distribution log_uniform_variance() computes the Log Uniform variance PDF parameter A = 2 PDF parameter B = 20 PDF mean = 7.8173 PDF variance = 24.8801 Sample size = 1000 Sample mean = 8.06549 Sample variance = 25.342 Sample maximum = 19.9825 Sample minimum = 2.02865 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 4.21514 0.0695309 0.833074 4.21514 -5.13308 0.0212638 0.0445087 -5.13308 3.07995 0.0964766 0.738845 3.07995 1.72076 0.121028 0.589132 1.72076 4.60612 0.0607313 0.858521 4.60612 0.0755922 0.118555 0.386463 0.0755922 0.888098 0.124902 0.486016 0.888098 -5.37511 0.0190329 0.0396368 -5.37511 -2.25586 0.0685903 0.164114 -2.25586 -0.593932 0.107078 0.310675 -0.593932 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 = 2.18475 Sample variance = 29.4359 Sample maximum = 24.7538 Sample minimum = -19.2367 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 0.234094 0.301773 0.573196 0.234094 0.538027 0.246853 0.657119 0.538027 0.318672 0.288965 0.598198 0.318672 3.17288 0.0287616 0.902815 3.17288 0.665896 0.220525 0.686997 0.665896 -0.428734 0.268885 0.371075 -0.428734 -0.541862 0.246062 0.341936 -0.541862 0.199855 0.306084 0.562789 0.199855 5.37967 0.0106313 0.941499 5.37967 0.262599 0.297776 0.581742 0.262599 lorentz_sample_test(): lorentz_mean() computes the Lorentz mean lorentz_variance() computes the Lorentz variance lorentz_sample() samples the Lorentz distribution. PDF mean = 0 PDF variance = 1.79769e+308 Sample size = 1000 Sample mean = 18.6183 Sample variance = 376607 Sample maximum = 19375.2 Sample minimum = -1134.19 maxwell_cdf_test(): 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 3.79709 0.237165 0.715775 3.79688 0.800306 0.0589648 0.150606 0.800293 4.10729 0.204245 0.749891 4.10742 4.94616 0.114627 0.824218 4.94531 2.89609 0.293192 0.592074 2.89648 3.738 0.242996 0.708819 3.73828 2.49332 0.285052 0.5235 2.49316 2.89807 0.293172 0.592391 2.89844 4.20121 0.193833 0.75946 4.20117 1.95931 0.236949 0.419105 1.95898 maxwell_sample_test(): maxwell_mean() computes the Maxwell mean maxwell_variance() computes the Maxwell variance maxwell_sample() samples the Maxwell distribution. PDF parameter A = 2 PDF mean = 3.19154 PDF mean = 1.81408 Sample size = 1000 Sample mean = 3.14034 Sample variance = 1.68939 Sample maximum = 8.25641 Sample minimum = 0.146357 multinomial_coef_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_pdf_test(): multinomial_pdf() evaluates the Multinomial PDF. PDF argument X: 0 0 1 2 2 3 PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 0: 0.1 1: 0.5 2: 0.4 PDF value = 0.16 multinomial_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 means and variances: 0.625 0.546875 2.5 1.25 1.875 1.17188 Sample size = 1000 Component Min, Max, Mean, Variance: 0 0 4 0.631 0.603442 1 0 5 2.526 1.34668 2 0 5 1.843 1.23359 multinoulli_pdf_test(): multinoulli_pdf() evaluates the Multinoulli PDF. X pdf(X) -1 0 0 0.0128056 1 0.126391 2 0.638504 3 0.0288851 4 0.193414 5 0 nakagami_cdf_test(): nakagami_cdf() evaluates the Nakagami CDF nakagami_pdf() evaluates the Nakagami PDF X PDF CDF CDf_inv 3.18257 0.586699 0.692394 3.18258 3.2582 0.540746 0.735053 3.2582 3.31623 0.503068 0.765346 3.31623 3.36515 0.470346 0.789159 3.36515 3.40825 0.441184 0.808803 3.40825 3.44721 0.414809 0.82548 3.44721 3.48305 0.390724 0.839911 3.48305 3.5164 0.36858 0.852572 3.5164 3.54772 0.348118 0.863796 3.54772 3.57735 0.329135 0.873828 3.57735 nakagami_sample_test(): nakagami_mean() computes the Nakagami mean nakagami_variance() computes the Nakagami variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 2.91874 PDF variance = 0.318446 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 7 0.0889893 0.555054 7 10 0.0563135 0.755975 10 12 0.0387155 0.841618 12 11 0.0469279 0.802903 11 6 0.098877 0.466064 6 5 0.105469 0.367188 5 12 0.0387155 0.841618 12 11 0.0469279 0.802903 11 6 0.098877 0.466064 6 5 0.105469 0.367188 5 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 = 2.719 Sample variance = 0.946039 Sample maximum = 10 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 0.194206 0.391489 0.576993 0.194206 2.14975 0.0395717 0.984212 2.14975 1.16797 0.201693 0.87859 1.16797 -0.615625 0.330075 0.269071 -0.615625 -0.225982 0.388885 0.410608 -0.225982 -0.299679 0.381425 0.382211 -0.299679 0.043373 0.398567 0.517298 0.043373 -0.710232 0.310009 0.23878 -0.710232 0.0810094 0.397635 0.532283 0.0810094 1.22945 0.187363 0.890548 1.22945 normal_01_cdf_values_test(): normal_01_cdf_values() stores values of the unit normal CDF. X normal_01_cdf(X) 0.000000 0.5000000000000000 0.100000 0.5398278372770290 0.200000 0.5792597094391030 0.300000 0.6179114221889526 0.400000 0.6554217416103242 0.500000 0.6914624612740131 0.600000 0.7257468822499270 0.700000 0.7580363477769270 0.800000 0.7881446014166033 0.900000 0.8159398746532405 1.000000 0.8413447460685429 1.500000 0.9331927987311419 2.000000 0.9772498680518208 2.500000 0.9937903346742240 3.000000 0.9986501019683699 3.500000 0.9997673709209645 4.000000 0.9999683287581669 normal_01_sample_test(): normal_01_mean() computes the Normal 01 mean normal_01_sample() samples the Normal 01 distribution normal_01_variance() returns the Normal 01 variance. PDF mean = 0 PDF variance = 1 Sample size = 1000 Sample mean = 0.0492474 Sample variance = 0.966278 Sample maximum = 2.84103 Sample minimum = -2.85516 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 97.7979 0.0263111 0.441642 97.7979 112.06 0.0192513 0.789294 112.06 109.545 0.0217215 0.737722 109.545 102.544 0.0262164 0.567333 102.544 95.8271 0.0255867 0.390433 95.8271 88.3385 0.0196596 0.218452 88.3385 85.4286 0.0165921 0.165667 85.4286 88.1608 0.019478 0.214974 88.1608 108.888 0.0223138 0.723261 108.888 105.408 0.0249228 0.640765 105.408 normal_sample_test(): normal_mean() computes the Normal mean normal_sample samples() the Normal distribution normal_variance() returns the Normal variance. PDF parameter MU = 100 PDF parameter SIGMA = 15 PDF mean = 100 PDF variance = 225 Sample size = 1000 Sample mean = 99.4773 Sample variance = 223.105 Sample maximum = 151.333 Sample minimum = 53.9498 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 71.932 0.00890183 0.113177 71.932 82.5539 0.0131053 0.230369 82.5539 103.699 0.0165364 0.561617 103.699 114.637 0.014085 0.731418 114.637 121.775 0.0114409 0.82281 121.775 112.267 0.0148223 0.697139 112.267 70.3898 0.00829038 0.0999218 70.3898 63.2152 0.00566331 0.0501228 63.2152 95.8755 0.0164924 0.431356 95.8755 104.788 0.0164146 0.579562 104.788 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 = 98.974 Sample variance = 482.773 Sample maximum = 149.334 Sample minimum = 50.7133 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 116.474 0.0131422 0.739109 116.474 120.528 0.011656 0.789425 120.528 112.306 0.0144661 0.681476 112.306 109.5 0.0151918 0.639829 109.5 76.0731 0.010329 0.149925 76.0731 59.3366 0.00434987 0.0298469 59.3366 108.545 0.0154026 0.625228 108.545 101.363 0.0163049 0.510606 101.363 76.705 0.0105786 0.156531 76.705 64.5529 0.00597604 0.0566513 64.5529 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 = 101.643 Sample variance = 515.567 Sample maximum = 176.684 Sample minimum = 50.478 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 101.336 0.0163059 0.533452 101.336 89.9469 0.0150609 0.351801 89.9469 122.148 0.011029 0.831077 122.148 83.6213 0.0131753 0.26215 83.6213 128.11 0.00867809 0.889825 128.11 119.785 0.011939 0.80393 119.785 91.6654 0.0154465 0.378022 91.6654 112.79 0.0143262 0.711723 112.79 92.9299 0.0156891 0.397711 92.9299 94.4669 0.0159341 0.42202 94.4669 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 = 98.8599 Sample variance = 555.556 Sample maximum = 149.881 Sample minimum = 12.271 owen_values_test(): owen_values() stores values of the OWEN function. H A T 0.062500 0.250000 0.038912 6.500000 0.437500 0.000000 7.000000 0.968750 0.000000 4.781250 0.062500 0.000000 2.000000 0.500000 0.008625 1.000000 0.999997 0.066742 1.000000 0.500000 0.043065 1.000000 1.000000 0.066742 1.000000 2.000000 0.078468 1.000000 3.000000 0.079300 0.500000 0.500000 0.064489 0.500000 1.000000 0.106671 0.500000 2.000000 0.141581 0.500000 3.000000 0.151084 0.250000 0.500000 0.071347 0.250000 1.000000 0.120129 0.250000 2.000000 0.166613 0.250000 3.000000 0.184750 0.125000 0.500000 0.073173 0.125000 1.000000 0.123763 0.125000 2.000000 0.173744 0.125000 3.000000 0.195119 0.007812 0.500000 0.073789 0.007812 1.000000 0.124995 0.007812 2.000000 0.176198 0.007812 3.000000 0.198777 0.007812 10.000000 0.234089 0.007812 100.000000 0.247946 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 0.701011 1.31665 0.815403 0.701011 0.531059 6.96567 0.260164 0.531059 0.899482 0.295029 0.946925 0.899482 0.779698 0.695443 0.891553 0.779698 0.535326 6.63914 0.289179 0.535326 0.517917 8.09583 0.161407 0.517917 0.542866 6.10468 0.337195 0.542866 0.502757 9.67545 0.0271195 0.502757 0.577726 4.20232 0.514442 0.577726 0.691401 1.43034 0.802213 0.691401 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 = 0.617799 Sample variance = 0.0205207 Sample maximum = 1.75631 Sample minimum = 0.50003 pearson_05_pdf_test(): pearson_05_pdf() evaluates the Pearson 05 PDF. PDF argument X = 5 PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF value = 0.0758163 planck_pdf_test(): planck_pdf() evaluates the Planck PDF. PDF parameter A = 2 PDF parameter B = 3 X PDF 1.62143 0.426826 1.67817 0.420621 1.23894 0.42924 1.15658 0.418598 1.19615 0.424271 1.82405 0.399789 2.69955 0.220118 2.34232 0.295166 0.976441 0.3792 3.13861 0.143377 planck_sample_test(): planck_mean() returns the mean of the Planck distribution. planck_sample() samples the Planck distribution. planck_variance() returns the variance of the Planck distribution. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 3.83223 PDF variance = 4.11319 Sample size = 1000 Sample mean = 1.90331 Sample variance = 0.897468 Sample maximum = 6.13467 Sample minimum = 0.176716 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 11 0.113736 0.696776 11 8 0.112599 0.33282 8 5 0.0378333 0.067086 5 17 0.012764 0.985722 17 7 0.0900792 0.220221 7 8 0.112599 0.33282 8 13 0.0729079 0.864464 13 13 0.0729079 0.864464 13 6 0.0630555 0.130141 6 7 0.0900792 0.220221 7 poisson_sample_test(): poisson_mean() computes the Poisson mean poisson_sample() samples the Poisson distribution poisson_variance() computes the Poisson variance. PDF parameter A = 10 PDF mean = 10 PDF variance = 10 Sample size = 1000 Sample mean = 9.756 Sample variance = 9.86646 Sample maximum = 22 Sample minimum = 1 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 2.69345 0.598545 0.806076 2.69345 2.5951 0.576689 0.748282 2.5951 1.78669 0.397042 0.354695 1.78669 2.86697 0.637104 0.91328 2.86697 0.901981 0.20044 0.0903965 0.901981 2.72882 0.606404 0.827383 2.72882 1.94368 0.43193 0.419768 1.94368 2.00017 0.444482 0.44452 2.00017 1.66518 0.37004 0.308091 1.66518 1.65414 0.367587 0.30402 1.65414 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 = 1.98711 Sample variance = 0.503291 Sample maximum = 2.99983 Sample minimum = 0.107342 psi_values_test(): psi_values() stores values of the PSI function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 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 1 0.212537 0.695037 2 3 0.0738088 0.894094 4 0 0.4825 0.4825 1 4 0.0434955 0.93759 5 0 0.4825 0.4825 1 3 0.0738088 0.894094 4 4 0.0434955 0.93759 5 4 0.0434955 0.93759 5 1 0.212537 0.695037 2 0 0.4825 0.4825 1 quasigeometric_sample_test(): quasigeometric_mean() computes the Quasigeometric mean quasigeometric_sample() samples the Quasigeometric distribution quasigeometric_variance() computes the Quasigeometric variance. PDF parameter A = 0.4825 PDF parameter B = 0.5893 PDF parameter A = 0.4825 PDF mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.3 Sample variance = 3.574 Sample maximum = 14 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 5 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 5 1 0.4 2.5 2.5 1 1 1 1 2 2 0.1666666666666667 0.1666666666666667 3 3 0.03333333333333333 0.03333333333333333 4 4 0.007142857142857143 0.007142857142857143 5 5 0.001587301587301587 0.001587301587301587 6 2 0.02380952380952381 0.02380952380952381 6 3 0.005952380952380952 0.005952380952380952 6 4 0.001984126984126984 0.001984126984126984 6 5 0.0007936507936507937 0.0007936507936507937 6 6 0.0003607503607503608 0.0003607503607503608 7 7 8.325008325008325e-05 8.325008325008325e-05 r8_csc_test(): r8_csc() computes the cosecant of an angle. ANGLE r8_csc(ANGLE) 0.00 Undefined 15.00 1.46037 30.00 -1.00194 45.00 1.29876 60.00 -8.05172 75.00 -1.69796 90.00 1.0177 105.00 -1.18588 120.00 4.05727 135.00 2.06607 150.00 -1.05049 165.00 1.10683 180.00 Undefined 195.00 -2.69119 210.00 1.10311 225.00 -1.05294 240.00 2.09321 255.00 3.94632 270.00 -1.18053 285.00 1.0191 300.00 -1.71484 315.00 -7.61642 330.00 1.29113 345.00 -1.00241 360.00 Undefined r8_erf_test(): r8_erf() evaluates the error function. X ERF(X) r8_erf(X) 0 0 0 0.1 0.1124629160182849 0.1124629160182849 0.2 0.2227025892104785 0.2227025892104785 0.3 0.3286267594591274 0.3286267594591273 0.4 0.4283923550466685 0.4283923550466684 0.5 0.5204998778130465 0.5204998778130465 0.6 0.6038560908479259 0.6038560908479259 0.7 0.6778011938374185 0.6778011938374184 0.8 0.7421009647076605 0.7421009647076605 0.9 0.7969082124228321 0.7969082124228322 1 0.8427007929497149 0.8427007929497148 1.1 0.8802050695740817 0.8802050695740817 1.2 0.9103139782296354 0.9103139782296354 1.3 0.9340079449406524 0.9340079449406524 1.4 0.9522851197626488 0.9522851197626487 1.5 0.9661051464753106 0.9661051464753108 1.6 0.976348383344644 0.976348383344644 1.7 0.9837904585907746 0.9837904585907746 1.8 0.9890905016357306 0.9890905016357308 1.9 0.9927904292352575 0.9927904292352574 2 0.9953222650189527 0.9953222650189527 r8_gamma_inc_test(): r8_gamma_inc() evaluates the normalized incomplete Gamma function P(A,X). A X Exact F r8_gamma_inc(A,X) 0.1 0.03 2.4903 0.738235 0.1 0.3 0.871837 0.908358 0.1 1.5 0.107921 0.988656 0.5 0.075 1.23812 0.301465 0.5 0.75 0.39113 0.779329 0.5 3.5 0.0144472 0.991849 1 0.1 0.904837 0.0951626 1 1 0.367879 0.632121 1 5 0.00673795 0.993262 1.1 0.1 0.882797 0.0720597 1.1 1 0.390833 0.589181 1.1 5 0.00805146 0.991537 2 0.15 0.989814 0.0101858 2 1.5 0.557825 0.442175 2 7 0.00729506 0.992705 6 2.5 114.957 0.042021 6 12 2.44092 0.979659 11 16 280855 0.922604 26 25 8.57648e+24 0.447079 41 45 2.08503e+47 0.744455 r8_zeta_test(): r8_zeta() estimates the Zeta function. P r8_zeta(P) 1 1.79769e+308 2 1.64493 3 1.20206 4 1.08232 5 1.03693 6 1.01734 7 1.00835 8 1.00408 9 1.00201 10 1.00099 11 1.00049 12 1.00025 13 1.00012 14 1.00006 15 1.00003 16 1.00002 17 1.00001 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 3 1.20206 3.125 1.17905 3.25 1.15915 3.375 1.14185 3.5 1.12673 3.625 1.11347 3.75 1.10179 3.875 1.09147 4 1.08232 r8poly_print_test(): r8poly_print() prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 r8poly_value_horner_test(): r8poly_value_horner() evaluates a polynomial at a point using Horner's method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X P(X) 0 0.0000 24 1 0.3333 10.8642 2 0.6667 3.45679 3 1.0000 0 4 1.3333 -0.987654 5 1.6667 -0.691358 6 2.0000 0 7 2.3333 0.493827 8 2.6667 0.493827 9 3.0000 0 10 3.3333 -0.691358 11 3.6667 -0.987654 12 4.0000 0 13 4.3333 3.45679 14 4.6667 10.8642 15 5.0000 24 r8row_max_test(): r8row_max() computes maximums of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 Row maximums: 0: 4 1: 8 2: 12 r8row_mean_test(): r8row_mean() computes row means of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 The row means: 0: 2.5 1: 6.5 2: 10.5 r8row_min_test(): r8row_min() computes minimums of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 Row minimums: 0: 1 1: 5 2: 9 r8row_variance_test(): r8row_variance() computes variances of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 The row variances: 0: 1.66667 1: 1.66667 2: 1.66667 r8vec_transpose_print_test(): r8vec_transpose_print() prints an R8VEC "tranposed", that is, placing multiple entries on a line. The vector X: 1 2.1 3.2 4.3 5.4 6.5 7.6 8.7 9.8 10.9 11 r8vec2_print_test(): r8vec2_print() prints a pair of R8VEC's. Print a pair of R8VEC's: 0: 0 0 1: 0.2 0.04 2: 0.4 0.16 3: 0.6 0.36 4: 0.8 0.64 5: 1 1 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 4.00086 0.135248 0.864781 4.00086 3.18621 0.223922 0.718886 3.18621 5.75574 0.0228876 0.984094 5.75574 1.42074 0.275979 0.222999 1.42074 0.85381 0.194862 0.0870954 0.85381 4.12806 0.122628 0.881176 4.12806 1.25383 0.257534 0.178408 1.25383 1.07999 0.233368 0.135668 1.07999 3.29546 0.211982 0.742698 3.29546 2.71176 0.270386 0.601165 2.71176 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 = 2.58912 Sample variance = 1.6899 Sample maximum = 7.43077 Sample minimum = 0.0740736 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 1.30384 0.698122 0.241499 1.30384 1.48304 0.613766 0.35872 1.48304 1.11843 0.813855 0.101878 1.11843 2.96666 0.306823 0.989826 2.96666 1.45319 0.626372 0.340214 1.45319 1.92327 0.473276 0.595322 1.92327 2.03462 0.447375 0.646552 2.03462 1.35227 0.673119 0.274696 1.35227 2.52345 0.360712 0.842542 2.52345 2.04564 0.444966 0.651466 2.04564 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 = 1.79922 Sample variance = 0.323578 Sample maximum = 2.99302 Sample minimum = 1.00022 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 9.76879 0.0107777 0.978428 9.76879 3.85332 0.145692 0.631868 3.85332 7.81524 0.0284268 0.94284 7.81524 7.38485 0.0351005 0.929217 7.38485 4.09228 0.13805 0.665793 4.09228 0.163459 0.0728047 0.151236 0.163459 5.91308 0.0703584 0.854243 5.91308 4.83 0.109865 0.757478 4.83 1.36012 0.117422 0.264128 1.36012 15.1884 0.000718088 0.998564 15.1884 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 = 3.04337 Sample variance = 8.75498 Sample maximum = 17.3778 Sample minimum = -11.3339 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 1.99985 0.275651 0.19546 2 2.51025 0.308619 0.345679 2.51025 4.27583 0.245133 0.876576 4.27588 2.74108 0.315631 0.417815 2.74121 4.68777 0.170781 0.963856 4.6875 1.81309 0.256197 0.145722 1.81348 3.37814 0.312569 0.619644 3.37793 2.96317 0.318256 0.488277 2.96289 4.3471 0.235276 0.893702 4.34668 4.73978 0.157004 0.972388 4.74023 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 = 3.03378 Sample variance = 0.981665 Sample maximum = 4.99073 Sample minimum = 1.07137 sin_power_int_test(): sin_power_int() returns values of the integral of SIN(X)^N from A to B. A B N Exact Computed 10.000000 20.000000 0 1.000000e+01 1.000000e+01 0.000000 1.000000 1 4.596977e-01 4.596977e-01 0.000000 1.000000 2 2.726756e-01 2.726756e-01 0.000000 1.000000 3 1.789406e-01 1.789406e-01 0.000000 1.000000 4 1.240256e-01 1.240256e-01 0.000000 1.000000 5 8.897440e-02 8.897440e-02 0.000000 2.000000 5 9.039312e-01 9.039312e-01 1.000000 2.000000 5 8.149568e-01 8.149568e-01 0.000000 1.000000 10 2.188752e-02 2.188752e-02 0.000000 1.000000 11 1.702344e-02 1.702344e-02 sin_power_int_values_test(): sin_power_int_values() stores values of the sine power integral. A B N F 10.000000 20.000000 0 10 0.000000 1.000000 1 0.4596976941318603 0.000000 1.000000 2 0.2726756432935796 0.000000 1.000000 3 0.1789405625488581 0.000000 1.000000 4 0.1240255653152068 0.000000 1.000000 5 0.08897439645157594 0.000000 2.000000 5 0.9039312384814995 1.000000 2.000000 5 0.8149568420299235 0.000000 1.000000 10 0.02188752242172985 0.000000 1.000000 11 0.01702343937406933 stirling2_number_test(): stirling2_number() calculates a Stirling number S2(n,k) of the second kind. 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 3 1 0 0 0 0 0 0 1 7 6 1 0 0 0 0 0 1 15 25 10 1 0 0 0 0 1 31 90 65 15 1 0 0 0 1 63 301 350 140 21 1 0 0 1 127 966 1701 1050 266 28 1 student_cdf_test(): student_cdf() evaluates the Student CDF. student_pdf() evaluates the Student PDF. PDF argument X = 2.447 PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF value = 0.14754 CDF value = 0.816049 student_sample_test(): student_mean() computes the Student mean student_sample() samples the Student distribution student_variance() computes the Student variance. PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF mean = 0.5 PDF variance = 6 Sample size = 1000 Sample mean = 0.425928 Sample variance = 2.59058 Sample maximum = 16.9105 Sample minimum = -13.9551 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 5.87891 0.130828 0.730422 5.87891 3.95594 0.191875 0.420148 3.95594 9.3069 0.0220032 0.992375 9.3069 4.80406 0.16495 0.571464 4.80406 5.3601 0.147298 0.658275 5.3601 8.52237 0.0469089 0.965343 8.52237 3.40097 0.209493 0.308774 3.40097 6.51872 0.110517 0.80763 6.51872 2.4758 0.163977 0.120999 2.4758 3.73309 0.19895 0.3766 3.73309 triangle_sample_test(): triangle_mean() returns the Triangle mean triangle_sample samples the Triangle distribution triangle_variance returns the Triangle variance PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 10 PDF parameter MEAN = 4.66667 PDF parameter VARIANCE = 3.72222 Sample size = 1000 Sample mean = 4.78956 Sample variance = 3.73249 Sample maximum = 9.73798 Sample minimum = 1.07036 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 6.86163 0.154981 0.756805 6.86163 4.59552 0.177557 0.319205 4.59552 7.18472 0.139026 0.804302 7.18472 3.21659 0.109461 0.121316 3.21659 5.16255 0.205558 0.427823 5.16255 4.76541 0.185946 0.350082 4.76541 8.87566 0.055523 0.968787 8.87566 3.80552 0.138544 0.194345 3.80552 3.73648 0.135135 0.184897 3.73648 7.24018 0.136287 0.811936 7.24018 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 = 5.47862 Sample variance = 3.07824 Sample maximum = 9.88846 Sample minimum = 1.17407 trigamma_test(): trigamma() evaluates the trigamma function. X FX FX Tabulated Computed 1 1.644934066848226 1.644934065473016 1.1 1.433299150792759 1.43329914968199 1.2 1.267377205423779 1.267377204522996 1.3 1.134253434996619 1.134253434263296 1.4 1.025356590529597 1.025356589930374 1.5 0.9348022005446793 0.9348022000532704 1.6 0.8584318931245799 0.8584318927201864 1.7 0.7932328301639984 0.793232829830095 1.8 0.7369741375017002 0.7369741372251055 1.9 0.6879720582426356 0.6879720580127948 2 0.6449340668482264 0.6449340654730159 trigamma_values_test(): trigamma_values() stores values of the trigamma function. X trigamma(X) 1.000000 1.6449340668482260 1.100000 1.4332991507927590 1.200000 1.2673772054237791 1.300000 1.1342534349966189 1.400000 1.0253565905295969 1.500000 0.9348022005446793 1.600000 0.8584318931245799 1.700000 0.7932328301639984 1.800000 0.7369741375017002 1.900000 0.6879720582426356 2.000000 0.6449340668482264 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 0.629986 1 0.629986 0.629986 0.525623 1 0.525623 0.525623 0.430585 1 0.430585 0.430585 0.0215938 1 0.0215938 0.0215938 0.239835 1 0.239835 0.239835 0.66758 1 0.66758 0.66758 0.112808 1 0.112808 0.112808 0.498565 1 0.498565 0.498565 0.615439 1 0.615439 0.615439 0.393473 1 0.393473 0.393473 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 = 0.478467 Sample variance = 0.085911 Sample maximum = 0.998512 Sample minimum = 0.00101913 uniform_01_order_sample_test(): uniform_order_sample() samples the Uniform 01 Order distribution. Ordered sample: 0: 0.199061 1: 0.355219 2: 0.358908 3: 0.385623 4: 0.453507 5: 0.454167 6: 0.458219 7: 0.598514 8: 0.863685 9: 0.911736 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 9.24944 0.111111 0.916605 9.24944 4.24964 0.111111 0.361071 4.24964 4.90423 0.111111 0.433803 4.90423 3.42617 0.111111 0.269574 3.42617 5.12423 0.111111 0.458248 5.12423 7.33283 0.111111 0.703647 7.33283 9.71993 0.111111 0.968881 9.71993 7.70811 0.111111 0.745345 7.70811 7.84707 0.111111 0.760785 7.84707 5.71436 0.111111 0.523818 5.71436 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 = 5.35256 Sample variance = 6.46923 Sample maximum = 9.97657 Sample minimum = 1.00026 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 6 0.166667 1 6 3 0.166667 0.5 4 5 0.166667 0.833333 6 3 0.166667 0.5 4 5 0.166667 0.833333 6 2 0.166667 0.333333 3 3 0.166667 0.5 4 3 0.166667 0.5 4 2 0.166667 0.333333 3 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 = 3.45 Sample variance = 2.8895 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: -0.550072 -0.285635 0.784751 0.374047 0.283349 0.883064 0.344024 -0.582645 0.736323 -0.324756 0.717301 0.616452 -0.0266752 0.508341 -0.860743 -0.254902 0.322899 0.911461 0.196736 0.965778 -0.16902 -0.0631838 0.742564 -0.666788 0.437578 0.625565 0.645905 0.0844842 -0.635656 -0.767336 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 4.06961 0.00949783 0.999319 4.06796 1.2649 0.481123 0.633537 1.265 -0.279474 0.124005 0.0650615 -0.27934 0.783115 0.492271 0.389838 0.782942 1.95193 0.222764 0.879282 1.95184 -0.0356523 0.193604 0.103305 -0.035437 2.29646 0.120025 0.937011 2.29621 1.77864 0.289926 0.834972 1.7785 1.10604 0.510123 0.554499 1.10584 2.24973 0.131242 0.931143 2.25019 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 = 1.0209 Sample circular variance = 0.299776 Sample maximum = 4.08868 Sample minimum = -2.07949 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 4.11956 0.366521 0.220554 4.11956 6.18265 0.0825922 0.977144 6.18265 5.74749 0.227687 0.912393 5.74749 5.16264 0.454268 0.709205 5.16264 5.12 0.465561 0.689587 5.12 5.03001 0.485257 0.646765 5.03001 3.77054 0.242774 0.114251 3.77054 4.11195 0.363878 0.217773 4.11195 5.27494 0.419209 0.758316 5.27494 5.01489 0.487986 0.639408 5.01489 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 = 4.71836 Sample variance = 0.553768 Sample maximum = 6.88307 Sample minimum = 2.16127 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 1 0.359214 0.859214 1 1 0.359214 0.859214 1 4 0.00347534 0.999569 5 3 0.0233711 0.996094 3 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 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 = 1.164 Sample variance = 0.215104 Sample maximum = 5 Sample minimum = 1 zipf_cdf_test(): zipf_pdf() evaluates the Zipf PDF. zipf_cdf() evaluates the Zipf CDF. zipf_cdf_inv() inverts the Zipf CDF. PDF parameter A = 2 X PDF(X) CDF(X) CDf_inv(CDF) 1 0.607927 0.607927 1 2 0.151982 0.759909 2 3 0.0675475 0.827456 3 4 0.0379954 0.865452 4 5 0.0243171 0.889769 5 6 0.0168869 0.906656 6 7 0.0124067 0.919062 7 8 0.00949886 0.928561 8 9 0.00750527 0.936067 9 10 0.00607927 0.942146 10 11 0.00502419 0.94717 11 12 0.00422172 0.951392 12 13 0.0035972 0.954989 13 14 0.00310167 0.958091 14 15 0.0027019 0.960792 15 16 0.00237472 0.963167 16 17 0.00210355 0.965271 17 18 0.00187632 0.967147 18 19 0.00168401 0.968831 19 20 0.00151982 0.970351 20 zipf_sample_test(): zipf_mean() returns the mean of the Zipf distribution. zipf_sample() samples the Zipf distribution. zipf_variance() returns the variance of the Zipf distribution. PDF parameter A = 4 PDF mean = 1.11063 PDF variance = 0.286326 Sample size = 1000 Sample mean = 1.116 Sample variance = 0.234544 Sample maximum = 7 Sample minimum = 1 prob_test(): Normal end of execution. Wed Oct 8 08:47:52 2025