Tue Oct 19 17:05:31 2021 prob_test(): Python version: 3.6.9 Test prob(). angle_cdf_test Python version: 3.6.9 angle_cdf evaluates the Angle CDF PDF parameter N = 5 PDF argument X = 0.5 CDF value = 0.0107809 angle_cdf_test Normal end of execution. angle_mean_test Python version: 3.6.9 angle_mean computes the Angle mean PDF parameter N = 5 PDF mean = 1.5708 angle_mean_test Normal end of execution. angle_pdf_test Python version: 3.6.9 angle_pdf evaluates the Angle PDF PDF parameter N = 5 PDF argument X = 0.5 PDF value = 0.0826466 angle_pdf_test Normal end of execution. anglit_cdf_test Python version: 3.6.9 anglit_cdf evaluates the Anglit CDF anglit_cdf_inv inverts the Anglit CDF. anglit_pdf evaluates the Anglit PDF X PDF CDF CDf_inv 0.17571 0.9073 0.672116 0.17571 0.5973 0.917438 0.965035 0.5973 0.434174 0.996562 0.881631 0.434174 0.206908 0.931754 0.701054 0.206908 -0.103892 0.546026 0.396854 -0.103892 0.340192 0.994491 0.814546 0.340192 -0.587133 -0.379141 0.0387968 -0.587133 0.381318 0.999741 0.845415 0.381318 0.177029 0.908407 0.673354 0.177029 -0.621355 -0.441538 0.0266696 -0.621355 anglit_cdf_test Normal end of execution. anglit_sample_test Python version: 3.6.9 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 = -0.00010186 Sample variance = 0.114613 Sample maximum = 0.765892 Sample minimum = -0.742185 anglit_sample_test Normal end of execution. arcsin_cdf_test Python version: 3.6.9 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 0.204089 0.325154 0.565423 0.204089 0.183988 0.323838 0.558901 0.183988 0.954332 1.06547 0.90343 0.954332 -0.974852 1.42835 0.0715365 -0.974852 -0.978193 1.53258 0.0665965 -0.978193 -0.230445 0.327114 0.425982 -0.230445 -0.619612 0.405538 0.28729 -0.619612 0.071995 0.319138 0.522937 0.0719951 -0.945451 0.977113 0.105622 -0.945451 0.090884 0.319633 0.528969 0.0908844 arcsin_cdf_test Normal end of execution. arcsin_sample_test Python version: 3.6.9 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 = 0.00856987 Sample variance = 0.511929 Sample maximum = 1 Sample minimum = -0.999983 PDF parameter A = 16 PDF mean = 0 PDF variance = 128 Sample size = 1000 Sample mean = 0.711161 Sample variance = 127.362 Sample maximum = 16 Sample minimum = -15.9996 arcsin_sample_test Normal end of execution. benford_cdf_test Python version: 3.6.9 benford_cdf evaluates the Benford CDF. N CDF(N) CDF(N) by summing 1 0.30103 0.30103 2 0.477121 0.477121 3 0.60206 0.60206 4 0.69897 0.69897 5 0.778151 0.778151 6 0.845098 0.845098 7 0.90309 0.90309 8 0.954243 0.954243 9 1 1 N CDF(N) CDF(N) by summing 10 0.0413927 0.0413927 11 0.0791812 0.0791812 12 0.113943 0.113943 13 0.146128 0.146128 14 0.176091 0.176091 15 0.20412 0.20412 16 0.230449 0.230449 17 0.255273 0.255273 18 0.278754 0.278754 19 0.30103 0.30103 20 0.322219 0.322219 21 0.342423 0.342423 22 0.361728 0.361728 23 0.380211 0.380211 24 0.39794 0.39794 25 0.414973 0.414973 26 0.431364 0.431364 27 0.447158 0.447158 28 0.462398 0.462398 29 0.477121 0.477121 30 0.491362 0.491362 31 0.50515 0.50515 32 0.518514 0.518514 33 0.531479 0.531479 34 0.544068 0.544068 35 0.556303 0.556303 36 0.568202 0.568202 37 0.579784 0.579784 38 0.591065 0.591065 39 0.60206 0.60206 40 0.612784 0.612784 41 0.623249 0.623249 42 0.633468 0.633468 43 0.643453 0.643453 44 0.653213 0.653213 45 0.662758 0.662758 46 0.672098 0.672098 47 0.681241 0.681241 48 0.690196 0.690196 49 0.69897 0.69897 50 0.70757 0.70757 51 0.716003 0.716003 52 0.724276 0.724276 53 0.732394 0.732394 54 0.740363 0.740363 55 0.748188 0.748188 56 0.755875 0.755875 57 0.763428 0.763428 58 0.770852 0.770852 59 0.778151 0.778151 60 0.78533 0.78533 61 0.792392 0.792392 62 0.799341 0.799341 63 0.80618 0.80618 64 0.812913 0.812913 65 0.819544 0.819544 66 0.826075 0.826075 67 0.832509 0.832509 68 0.838849 0.838849 69 0.845098 0.845098 70 0.851258 0.851258 71 0.857332 0.857332 72 0.863323 0.863323 73 0.869232 0.869232 74 0.875061 0.875061 75 0.880814 0.880814 76 0.886491 0.886491 77 0.892095 0.892095 78 0.897627 0.897627 79 0.90309 0.90309 80 0.908485 0.908485 81 0.913814 0.913814 82 0.919078 0.919078 83 0.924279 0.924279 84 0.929419 0.929419 85 0.934498 0.934498 86 0.939519 0.939519 87 0.944483 0.944483 88 0.94939 0.94939 89 0.954243 0.954243 90 0.959041 0.959041 91 0.963788 0.963788 92 0.968483 0.968483 93 0.973128 0.973128 94 0.977724 0.977724 95 0.982271 0.982271 96 0.986772 0.986772 97 0.991226 0.991226 98 0.995635 0.995635 99 1 1 benford_cdf_test Normal end of execution. benford_pdf_test Python version: 3.6.9 benford_pdf evaluates the Benford PDF. N PDF(N) 1 0.30103 2 0.176091 3 0.124939 4 0.09691 5 0.0791812 6 0.0669468 7 0.0579919 8 0.0511525 9 0.0457575 N PDF(N) 10 0.0413927 11 0.0377886 12 0.0347621 13 0.0321847 14 0.0299632 15 0.0280287 16 0.0263289 17 0.0248236 18 0.0234811 19 0.0222764 20 0.0211893 21 0.0202034 22 0.0193052 23 0.0184834 24 0.0177288 25 0.0170333 26 0.0163904 27 0.0157943 28 0.01524 29 0.0147233 30 0.0142404 31 0.0137883 32 0.013364 33 0.012965 34 0.0125891 35 0.0122345 36 0.0118992 37 0.0115819 38 0.011281 39 0.0109954 40 0.0107239 41 0.0104654 42 0.0102192 43 0.00998422 44 0.00975984 45 0.00954532 46 0.00934003 47 0.00914338 48 0.00895484 49 0.00877392 50 0.00860017 51 0.00843317 52 0.00827253 53 0.00811789 54 0.00796893 55 0.00782534 56 0.00768683 57 0.00755314 58 0.00742402 59 0.00729924 60 0.00717858 61 0.00706185 62 0.00694886 63 0.00683942 64 0.00673338 65 0.00663058 66 0.00653087 67 0.00643411 68 0.00634018 69 0.00624895 70 0.00616031 71 0.00607415 72 0.00599036 73 0.00590886 74 0.00582954 75 0.00575233 76 0.00567713 77 0.00560388 78 0.00553249 79 0.0054629 80 0.00539503 81 0.00532883 82 0.00526424 83 0.00520119 84 0.00513964 85 0.00507953 86 0.0050208 87 0.00496342 88 0.00490733 89 0.0048525 90 0.00479888 91 0.00474644 92 0.00469512 93 0.00464491 94 0.00459575 95 0.00454763 96 0.0045005 97 0.00445434 98 0.00440912 99 0.00436481 benford_pdf_test Normal end of execution. bernoulli_cdf_test Python version: 3.6.9 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 0 0.25 0.25 0 0 0.25 0.25 0 0 0.25 0.25 0 1 0.75 1 1 1 0.75 1 1 1 0.75 1 1 1 0.75 1 1 bernoulli_cdf_test Normal end of execution. bernoulli_sample_test Python version: 3.6.9 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 = 0.745 Sample variance = 0.189975 Sample maximum = 1 Sample minimum = 0 bernoulli_sample_test Normal end of execution. bessel_i0_test: Python version: 3.6.9 bessel_i0 evaluates the Bessel function I0(X) X Exact F I0(X) 0 1 1 0.2 1.010025027795146 1.010025027795146 0.4 1.040401782229341 1.040401782229341 0.6 1.09204536431734 1.092045364317339 0.8 1.166514922869803 1.166514922869803 1 1.266065877752008 1.266065877752008 1.2 1.393725584134064 1.393725584134064 1.4 1.553395099731217 1.553395099731216 1.6 1.749980639738909 1.749980639738909 1.8 1.989559356618051 1.989559356618051 2 2.279585302336067 2.279585302336067 2.5 3.289839144050123 3.289839144050123 3 4.880792585865024 4.880792585865024 3.5 7.37820343222548 7.37820343222548 4 11.30192195213633 11.30192195213633 4.5 17.48117185560928 17.48117185560928 5 27.23987182360445 27.23987182360445 6 67.23440697647798 67.23440697647796 8 427.5641157218048 427.5641157218047 10 2815.716628466254 2815.716628466254 bessel_i0_test Normal end of execution. bessel_i0_values_test: Python version: 3.6.9 bessel_i0_values stores values of the Bessel I function. of order 0. X I(0,X) 0.000000 1 0.200000 1.010025027795146 0.400000 1.040401782229341 0.600000 1.09204536431734 0.800000 1.166514922869803 1.000000 1.266065877752008 1.200000 1.393725584134064 1.400000 1.553395099731217 1.600000 1.749980639738909 1.800000 1.989559356618051 2.000000 2.279585302336067 2.500000 3.289839144050123 3.000000 4.880792585865024 3.500000 7.37820343222548 4.000000 11.30192195213633 4.500000 17.48117185560928 5.000000 27.23987182360445 6.000000 67.23440697647798 8.000000 427.5641157218048 10.000000 2815.716628466254 bessel_i0_values_test: Normal end of execution. bessel_i1_test: Python version: 3.6.9 bessel_i1 evaluates the Bessel function I1(X) X Exact F I1(X) 0.000000 0 0 0.200000 0.1005008340281251 0.1005008340281251 0.400000 0.2040267557335706 0.2040267557335706 0.600000 0.3137040256049221 0.3137040256049221 0.800000 0.4328648026206398 0.4328648026206398 1.000000 0.565159103992485 0.5651591039924849 1.200000 0.7146779415526431 0.7146779415526432 1.400000 0.8860919814143274 0.8860919814143273 1.600000 1.08481063512988 1.08481063512988 1.800000 1.317167230391899 1.317167230391899 2.000000 1.590636854637329 1.590636854637329 2.500000 2.516716245288698 2.516716245288698 3.000000 3.953370217402609 3.953370217402608 3.500000 6.205834922258365 6.205834922258364 4.000000 9.759465153704451 9.759465153704447 4.500000 15.38922275373592 15.38922275373592 5.000000 24.33564214245053 24.33564214245052 6.000000 61.34193677764024 61.34193677764024 8.000000 399.8731367825601 399.8731367825602 10.000000 2670.988303701255 2670.988303701254 bessel_i1_test Normal end of execution. bessel_i1_values_test: Python version: 3.6.9 bessel_i1_values stores values of the Bessel I function. of order 1. X I(1,X) 0.000000 0 0.200000 0.1005008340281251 0.400000 0.2040267557335706 0.600000 0.3137040256049221 0.800000 0.4328648026206398 1.000000 0.565159103992485 1.200000 0.7146779415526431 1.400000 0.8860919814143274 1.600000 1.08481063512988 1.800000 1.317167230391899 2.000000 1.590636854637329 2.500000 2.516716245288698 3.000000 3.953370217402609 3.500000 6.205834922258365 4.000000 9.759465153704451 4.500000 15.38922275373592 5.000000 24.33564214245053 6.000000 61.34193677764024 8.000000 399.8731367825601 10.000000 2670.988303701255 bessel_i1_values_test: Normal end of execution. beta_binomial_cdf_test Python version: 3.6.9 beta_binomial_cdf evaluates the Beta Binomial CDF beta_binomial_cdf_inv inverts the Beta Binomial CDF. beta_binomial_pdf evaluates the Beta Binomial PDF PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 X PDF CDF CDf_inv 1 0.285714 0.5 1 1 0.285714 0.5 1 2 0.257143 0.757143 2 3 0.171429 0.928571 3 1 0.285714 0.5 1 3 0.171429 0.928571 3 1 0.285714 0.5 1 0 0.214286 0.214286 0 0 0.214286 0.214286 0 1 0.285714 0.5 1 beta_binomial_cdf_test Normal end of execution. beta_binomial_sample_test Python version: 3.6.9 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 = 1.689 Sample variance = 1.52028 Sample maximum = 4 Sample minimum = 0 beta_binomial_sample_test Normal end of execution. beta_cdf_test Python version: 3.6.9 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 0.547248 3.50487 0.676945 0.547248 12 12 0.58916 2.71113 0.808274 0.58916 12 12 0.409271 2.67654 0.187498 0.409271 12 12 0.264407 0.244456 0.00755495 0.264407 12 12 0.374713 1.89557 0.108478 0.374713 12 12 0.417876 2.86337 0.211341 0.417876 12 12 0.41191 2.73457 0.194638 0.41191 12 12 0.539247 3.61408 0.648454 0.539247 12 12 0.606755 2.3154 0.852516 0.606755 12 12 0.336835 1.12101 0.0518662 0.336835 beta_cdf_test Normal end of execution. beta_cdf_values_test: Python version: 3.6.9 beta_cdf_values stores values of the BETA function. A B X beta_cdf(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_cdf_values_test: Normal end of execution. beta_inc_test: Python version: 3.6.9 beta_inc evaluates the normalized incomplete Beta function beta_inc(A,B,X). A B X Exact F beta_inc(A,B,X) 0.5 0.5 0.01 0.0637686 0.0637686 0.5 0.5 0.1 0.204833 0.204833 0.5 0.5 1 1 1 1 0.5 0 0 0 1 0.5 0.01 0.00501256 0.00501256 1 0.5 0.1 0.0513167 0.0513167 1 0.5 0.5 0.292893 0.292893 1 1 0.5 0.5 0.5 2 2 0.1 0.028 0.028 2 2 0.2 0.104 0.104 2 2 0.3 0.216 0.216 2 2 0.4 0.352 0.352 2 2 0.5 0.5 0.5 2 2 0.6 0.648 0.648 2 2 0.7 0.784 0.784 2 2 0.8 0.896 0.896 2 2 0.9 0.972 0.972 5.5 5 0.5 0.436191 0.436191 10 0.5 0.9 0.151641 0.151641 10 5 0.5 0.0897827 0.0897827 10 5 1 1 1 10 10 0.5 0.5 0.5 20 5 0.8 0.459877 0.459877 20 10 0.6 0.214682 0.214682 20 10 0.8 0.950736 0.950736 20 20 0.5 0.5 0.5 20 20 0.6 0.897941 0.897941 30 10 0.7 0.22413 0.22413 30 10 0.8 0.758641 0.758641 40 20 0.7 0.700178 0.700178 1 0.5 0.1 0.0513167 0.0513167 1 0.5 0.2 0.105573 0.105573 1 0.5 0.3 0.16334 0.16334 1 0.5 0.4 0.225403 0.225403 1 2 0.2 0.36 0.36 1 3 0.2 0.488 0.488 1 4 0.2 0.5904 0.5904 1 5 0.2 0.67232 0.67232 2 2 0.3 0.216 0.216 3 2 0.3 0.0837 0.0837 4 2 0.3 0.03078 0.03078 5 2 0.3 0.010935 0.010935 1.30625 11.7562 0.225609 0.918885 0.918885 1.30625 11.7562 0.0335568 0.21053 0.21053 1.30625 11.7562 0.0295222 0.182413 0.182413 beta_inc_test Normal end of execution. beta_inc_values_test: Python version: 3.6.9 beta_inc_values stores values of the BETA function. A B X beta_inc(A,B,X) 0.500000 0.500000 0.010000 0.06376856085851985 0.500000 0.500000 0.100000 0.2048327646991335 0.500000 0.500000 1.000000 1 1.000000 0.500000 0.000000 0 1.000000 0.500000 0.010000 0.005012562893380045 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.500000 0.2928932188134525 1.000000 1.000000 0.500000 0.5 2.000000 2.000000 0.100000 0.028 2.000000 2.000000 0.200000 0.104 2.000000 2.000000 0.300000 0.216 2.000000 2.000000 0.400000 0.352 2.000000 2.000000 0.500000 0.5 2.000000 2.000000 0.600000 0.648 2.000000 2.000000 0.700000 0.784 2.000000 2.000000 0.800000 0.896 2.000000 2.000000 0.900000 0.972 5.500000 5.000000 0.500000 0.4361908850559777 10.000000 0.500000 0.900000 0.1516409096347099 10.000000 5.000000 0.500000 0.08978271484375 10.000000 5.000000 1.000000 1 10.000000 10.000000 0.500000 0.5 20.000000 5.000000 0.800000 0.4598773297575791 20.000000 10.000000 0.600000 0.2146816102371739 20.000000 10.000000 0.800000 0.9507364826957875 20.000000 20.000000 0.500000 0.5 20.000000 20.000000 0.600000 0.8979413687105918 30.000000 10.000000 0.700000 0.2241297491808366 30.000000 10.000000 0.800000 0.7586405487192086 40.000000 20.000000 0.700000 0.7001783247477069 1.000000 0.500000 0.100000 0.0513167019494862 1.000000 0.500000 0.200000 0.1055728090000841 1.000000 0.500000 0.300000 0.1633399734659245 1.000000 0.500000 0.400000 0.2254033307585166 1.000000 2.000000 0.200000 0.36 1.000000 3.000000 0.200000 0.488 1.000000 4.000000 0.200000 0.5904 1.000000 5.000000 0.200000 0.67232 2.000000 2.000000 0.300000 0.216 3.000000 2.000000 0.300000 0.0837 4.000000 2.000000 0.300000 0.03078 5.000000 2.000000 0.300000 0.010935 1.306250 11.756200 0.225609 0.918884684620518 1.306250 11.756200 0.033557 0.21052977489419 1.306250 11.756200 0.029522 0.1824130512500673 beta_inc_values_test: Normal end of execution. beta_sample_test Python version: 3.6.9 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 = 0.402433 Sample variance = 0.0412829 Sample maximum = 0.920221 Sample minimum = 0.0135483 beta_sample_test Normal end of execution. beta_values_test: Python version: 3.6.9 beta_values stores values of the BETA function. X Y BETA(X,Y) 0.200000 1.000000 5 0.400000 1.000000 2.5 0.600000 1.000000 1.666666666666667 0.800000 1.000000 1.25 1.000000 0.200000 5 1.000000 0.400000 2.5 1.000000 1.000000 1 2.000000 2.000000 0.1666666666666667 3.000000 3.000000 0.03333333333333333 4.000000 4.000000 0.007142857142857143 5.000000 5.000000 0.001587301587301587 6.000000 2.000000 0.02380952380952381 6.000000 3.000000 0.005952380952380952 6.000000 4.000000 0.001984126984126984 6.000000 5.000000 0.0007936507936507937 6.000000 6.000000 0.0003607503607503608 7.000000 7.000000 8.325008325008325e-05 beta_values_test: Normal end of execution. binomial_cdf_test Python version: 3.6.9 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 2 0.181147 0.235169 2 4 0.312386 0.883971 4 3 0.336416 0.571585 3 3 0.336416 0.571585 3 2 0.181147 0.235169 2 3 0.336416 0.571585 3 5 0.116029 1 5 5 0.116029 1 5 4 0.312386 0.883971 4 3 0.336416 0.571585 3 binomial_cdf_test Normal end of execution. binomial_sample_test Python version: 3.6.9 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 = 1.521 Sample variance = 1.08156 Sample maximum = 5 Sample minimum = 0 binomial_sample_test Normal end of execution. birthday_cdf_test Python version: 3.6.9 birthday_cdf evaluates the Birthday CDF birthday_cdf_inv inverts the Birthday CDF. birthday_pdf evaluates the Birthday PDF N PDF CDF CDf_inv 1 0 0 1 2 0.00273973 0.00273973 2 3 0.00546444 0.00820417 3 4 0.00815175 0.0163559 4 5 0.0107797 0.0271356 5 6 0.0133269 0.0404625 6 7 0.0157732 0.0562357 7 8 0.0180996 0.0743353 8 9 0.0202885 0.0946238 9 10 0.0223243 0.116948 10 11 0.0241932 0.141141 11 12 0.0258834 0.167025 12 13 0.0273855 0.19441 13 14 0.0286922 0.223103 14 15 0.0297988 0.252901 15 16 0.0307027 0.283604 16 17 0.0314037 0.315008 17 18 0.0319038 0.346911 18 19 0.0322071 0.379119 19 20 0.0323199 0.411438 20 21 0.03225 0.443688 21 22 0.032007 0.475695 22 23 0.0316019 0.507297 23 24 0.031047 0.538344 24 25 0.0303554 0.5687 25 26 0.0295411 0.598241 26 27 0.0286185 0.626859 27 28 0.0276022 0.654461 28 29 0.0265071 0.680969 29 30 0.0253477 0.706316 30 birthday_cdf_test Normal end of execution. birthday_sample_test Python version: 3.6.9 birthday_sample samples the Birthday distribution. N Mean PDF 10 0.02 0.0223243 11 0.025 0.0241932 12 0.027 0.0258834 13 0.031 0.0273855 14 0.033 0.0286922 15 0.036 0.0297988 16 0.037 0.0307027 17 0.035 0.0314037 18 0.025 0.0319038 19 0.039 0.0322071 20 0.036 0.0323199 21 0.037 0.03225 22 0.032 0.032007 23 0.031 0.0316019 24 0.029 0.031047 25 0.026 0.0303554 26 0.03 0.0295411 27 0.027 0.0286185 28 0.032 0.0276022 29 0.029 0.0265071 30 0.022 0.0253477 31 0.022 0.0241384 32 0.024 0.0228929 33 0.017 0.0216243 34 0.019 0.020345 35 0.019 0.0190664 36 0.021 0.0177989 37 0.014 0.0165519 38 0.021 0.0153338 39 0.012 0.0141518 40 0.013 0.0130121 birthday_sample_test Normal end of execution. bradford_cdf_test Python version: 3.6.9 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 1.08987 1.70448 0.1722 1.08987 1.37374 1.02019 0.542445 1.37374 1.34839 1.05813 0.516107 1.34839 1.20788 1.33283 0.34962 1.20788 1.50072 0.864871 0.661586 1.50072 1.16099 1.45927 0.28424 1.16099 1.00594 2.12614 0.0127446 1.00594 1.14817 1.49811 0.265292 1.14817 1.75499 0.662809 0.853532 1.75499 1.29583 1.14652 0.458234 1.29583 bradford_cdf_test Normal end of execution. bradford_sample_test Python version: 3.6.9 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 = 1.39136 Sample variance = 0.081761 Sample maximum = 1.99993 Sample minimum = 1.00004 bradford_sample_test Normal end of execution. buffon_box_pdf_test Python version: 3.6.9 buffon_box_pdf evaluates the Buffon-Laplace PDF, the probability that, on a grid of cells of width A and height B, a needle of length L, dropped at random, will cross at least one grid line. A B L PDF 1 1 0 0 1 1 0.2 0.241916 1 1 0.4 0.458366 1 1 0.6 0.649352 1 1 0.8 0.814873 1 1 1 0.95493 1 2 0 0 1 2 0.2 0.18462 1 2 0.4 0.356507 1 2 0.6 0.515662 1 2 0.8 0.662085 1 2 1 0.795775 1 3 0 0 1 3 0.2 0.165521 1 3 0.4 0.322554 1 3 0.6 0.471099 1 3 0.8 0.611155 1 3 1 0.742723 1 4 0 0 1 4 0.2 0.155972 1 4 0.4 0.305577 1 4 0.6 0.448817 1 4 0.8 0.58569 1 4 1 0.716197 1 5 0 0 1 5 0.2 0.150242 1 5 0.4 0.295392 1 5 0.6 0.435448 1 5 0.8 0.570411 1 5 1 0.700282 2 1 0 0 2 1 0.2 0.18462 2 1 0.4 0.356507 2 1 0.6 0.515662 2 1 0.8 0.662085 2 1 1 0.795775 2 2 0 0 2 2 0.4 0.241916 2 2 0.8 0.458366 2 2 1.2 0.649352 2 2 1.6 0.814873 2 2 2 0.95493 2 3 0 0 2 3 0.4 0.203718 2 3 0.8 0.39046 2 3 1.2 0.560225 2 3 1.6 0.713014 2 3 2 0.848826 2 4 0 0 2 4 0.4 0.18462 2 4 0.8 0.356507 2 4 1.2 0.515662 2 4 1.6 0.662085 2 4 2 0.795775 2 5 0 0 2 5 0.4 0.173161 2 5 0.8 0.336135 2 5 1.2 0.488924 2 5 1.6 0.631527 2 5 2 0.763944 3 1 0 0 3 1 0.2 0.165521 3 1 0.4 0.322554 3 1 0.6 0.471099 3 1 0.8 0.611155 3 1 1 0.742723 3 2 0 0 3 2 0.4 0.203718 3 2 0.8 0.39046 3 2 1.2 0.560225 3 2 1.6 0.713014 3 2 2 0.848826 3 3 0 0 3 3 0.6 0.241916 3 3 1.2 0.458366 3 3 1.8 0.649352 3 3 2.4 0.814873 3 3 3 0.95493 3 4 0 0 3 4 0.6 0.213268 3 4 1.2 0.407437 3 4 1.8 0.582507 3 4 2.4 0.738479 3 4 3 0.875352 3 5 0 0 3 5 0.6 0.196079 3 5 1.2 0.376879 3 5 1.8 0.5424 3 5 2.4 0.692642 3 5 3 0.827606 4 1 0 0 4 1 0.2 0.155972 4 1 0.4 0.305577 4 1 0.6 0.448817 4 1 0.8 0.58569 4 1 1 0.716197 4 2 0 0 4 2 0.4 0.18462 4 2 0.8 0.356507 4 2 1.2 0.515662 4 2 1.6 0.662085 4 2 2 0.795775 4 3 0 0 4 3 0.6 0.213268 4 3 1.2 0.407437 4 3 1.8 0.582507 4 3 2.4 0.738479 4 3 3 0.875352 4 4 0 0 4 4 0.8 0.241916 4 4 1.6 0.458366 4 4 2.4 0.649352 4 4 3.2 0.814873 4 4 4 0.95493 4 5 0 0 4 5 0.8 0.218997 4 5 1.6 0.417623 4 5 2.4 0.595876 4 5 3.2 0.753758 4 5 4 0.891268 5 1 0 0 5 1 0.2 0.150242 5 1 0.4 0.295392 5 1 0.6 0.435448 5 1 0.8 0.570411 5 1 1 0.700282 5 2 0 0 5 2 0.4 0.173161 5 2 0.8 0.336135 5 2 1.2 0.488924 5 2 1.6 0.631527 5 2 2 0.763944 5 3 0 0 5 3 0.6 0.196079 5 3 1.2 0.376879 5 3 1.8 0.5424 5 3 2.4 0.692642 5 3 3 0.827606 5 4 0 0 5 4 0.8 0.218997 5 4 1.6 0.417623 5 4 2.4 0.595876 5 4 3.2 0.753758 5 4 4 0.891268 5 5 0 0 5 5 1 0.241916 5 5 2 0.458366 5 5 3 0.649352 5 5 4 0.814873 5 5 5 0.95493 buffon_box_pdf_test Normal end of execution. buffon_box_sample_test Python version: 3.6.9 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 8 3.75 0.608407 100 99 3.0303 0.11129 10000 9554 3.14005 0.0015466 1000000 954670 3.14245 0.000854475 buffon_box_sample_test Normal end of execution. buffon_pdf_test Python version: 3.6.9 buffon_pdf evaluates the Buffon PDF, the probability that, on a grid of cells of width A, a needle of length L, dropped at random, will cross at least one grid line. A L PDF 1 0 0 1 0.2 0.127324 1 0.4 0.254648 1 0.6 0.381972 1 0.8 0.509296 1 1 0.63662 2 0 0 2 0.4 0.127324 2 0.8 0.254648 2 1.2 0.381972 2 1.6 0.509296 2 2 0.63662 3 0 0 3 0.6 0.127324 3 1.2 0.254648 3 1.8 0.381972 3 2.4 0.509296 3 3 0.63662 4 0 0 4 0.8 0.127324 4 1.6 0.254648 4 2.4 0.381972 4 3.2 0.509296 4 4 0.63662 5 0 0 5 1 0.127324 5 2 0.254648 5 3 0.381972 5 4 0.509296 5 5 0.63662 buffon_pdf_test Normal end of execution. buffon_sample_test Python version: 3.6.9 buffon_sample simulates a Buffon-Laplace needle dropping experiment. On a grid of cells of width A, a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1 Needle length L = 1 Trials Hits Est(Pi) Err 10 8 2.5 0.641593 100 68 2.94118 0.200416 10000 6344 3.15259 0.0109925 1000000 636800 3.1407 0.000889136 buffon_sample_test Normal end of execution. burr_cdf_test Python version: 3.6.9 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 3.65529 0.1419 0.910368 3.65529 3.01545 0.367782 0.755737 3.01545 3.36445 0.224716 0.857852 3.36445 1.98659 0.519562 0.202862 1.98659 2.76667 0.485613 0.649562 2.76667 3.33478 0.235065 0.851033 3.33478 1.706 0.328539 0.0824927 1.706 3.58693 0.158455 0.900111 3.58693 1.63565 0.275627 0.0612429 1.63565 3.18083 0.294511 0.810388 3.18083 burr_Df_test Normal end of execution. burr_sample_test Python version: 3.6.9 burr_mean computes the Burr mean burr_variance computes the Burr variance burr_sample Burr samples the distribution PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF parameter D = 2 PDF mean = 2.61227 PDF variance = 0.62513 Sample size = 1000 Sample mean = 2.636699 Sample variance = 0.687808 Sample maximum = 10.990195 Sample minimum = 1.169004 burr_sample_test Normal end of execution. cardioid_cdf_test Python version: 3.6.9 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 -2.47798 0.0964661 0.0566003 -2.47798 2.41764 0.099536 0.937488 2.41764 -1.47129 0.16706 0.186653 -1.47129 -1.82748 0.138952 0.132177 -1.82748 0.130815 0.238052 0.5312 0.130815 1.65775 0.152244 0.843116 1.65775 -0.634773 0.223231 0.351784 -0.634773 -1.6454 0.153224 0.15877 -1.6454 -0.188905 0.237317 0.454992 -0.188905 2.61613 0.0903132 0.956287 2.61612 cardioid_cdf_test Normal end of execution. cardioid_sample_test Python version: 3.6.9 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 = -0.108424 Sample variance = 2.13705 Sample maximum = 3.14094 Sample minimum = -3.13799 cardioid_sample_test Normal end of execution. cauchy_cdf_test Python version: 3.6.9 cauchy_cdf evaluates the Cauchy CDF cauchy_cdf_inv inverts the Cauchy CDF. cauchy_pdf evaluates the Cauchy PDF PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDf_inv 1.59214 0.104178 0.456989 1.59214 52.6629 0.000370741 0.981173 52.6629 3.73532 0.0795025 0.666926 3.73532 2.91935 0.0969945 0.594653 2.91935 -11.7677 0.0048095 0.0682924 -11.7677 -12.6368 0.00427766 0.0643504 -12.6368 0.100412 0.0757374 0.320323 0.100412 3.14165 0.0926814 0.615746 3.14165 2.5378 0.1028 0.556462 2.5378 2.67833 0.100943 0.570783 2.67833 cauchy_cdf_test Normal end of execution. cauchy_sample_test Python version: 3.6.9 cauchy_mean computes the Cauchy mean cauchy_variance computes the Cauchy variance cauchy_sample samples the Cauchy distribution. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 1.79769e+308 Sample size = 1000 Sample mean = 3.97206 Sample variance = 4849.32 Sample maximum = 1684.62 Sample minimum = -798.367 cauchy_sample_test Normal end of execution. chebyshev1_cdf_test Python version: 3.6.9 chebyshev1_cdf evaluates the Chebyshev1 CDF chebyshev1_cdf_inv inverts the Chebyshev1 CDF. chebyshev1_pdf evaluates the Chebyshev1 PDF X PDF CDF CDf_inv -0.916677 0.796515 0.130861 -0.916677 0.886009 0.686505 0.846533 0.886009 0.765213 0.494441 0.777367 0.765213 0.360207 0.341215 0.617294 0.360207 -0.435257 0.353557 0.356658 -0.435257 0.165998 0.322788 0.553085 0.165998 -0.441859 0.354827 0.354319 -0.441859 -0.937635 0.915677 0.113011 -0.937635 0.912572 0.778422 0.865907 0.912572 -0.936893 0.910457 0.113688 -0.936893 chebyshev1_cdf_test Normal end of execution. chebyshev1_sample_test Python version: 3.6.9 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 = -0.0109385 Sample variance = 0.518737 Sample maximum = 0.999985 Sample minimum = -0.999933 chebyshev1_sample_test Normal end of execution. chi_cdf_test Python version: 3.6.9 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 3.37177 0.277725 0.295946 3.37207 4.76979 0.239882 0.686026 4.76953 3.87295 0.293381 0.440659 3.87305 2.91878 0.231757 0.179505 2.91895 2.04434 0.0949134 0.0349149 2.04492 5.0435 0.211243 0.747828 5.04395 4.0513 0.289992 0.492747 4.05127 6.55725 0.0648679 0.94785 6.55859 2.99473 0.241332 0.197475 2.99512 4.26169 0.280672 0.552873 4.26172 chi_cdf_test Normal end of execution. chi_sample_test Python version: 3.6.9 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 = 4.22295 Sample variance = 1.7682 Sample maximum = 9.64062 Sample minimum = 1.29266 chi_sample_test Normal end of execution. chi_square_cdf_test Python version: 3.6.9 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 2.8205 0.172109 0.588299 3.95814 2.88487 0.170461 0.577273 3.8783 1.46662 0.176111 0.832537 6.45789 6.55365 0.0618466 0.161441 1.43232 1.14812 0.161665 0.886564 7.46113 4.32222 0.124477 0.364151 2.54919 4.04703 0.133744 0.399678 2.75099 3.3974 0.155364 0.493649 3.31632 2.1403 0.183508 0.709972 4.97349 8.03795 0.0361132 0.0901978 0.999959 chi_square_cdf_test Normal end of execution. chi_square_sample_test Python version: 3.6.9 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 = 10.0783 Sample variance = 19.5461 Sample maximum = 30.6549 Sample minimum = 1.37813 chi_square_sample_test Normal end of execution. chi_square_noncentral_sample_test Python version: 3.6.9 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 = 4.83109 Sample variance = 12.3753 Sample maximum = 23.8931 Sample minimum = 0.0809717 chi_square_noncentral_sample_test Normal end of execution. circular_normal_sample_test Python version: 3.6.9 circular_normal_mean computes the Circular Normal mean circular_normal_sample samples the Circular Normal distribution circular_normal_variance computes the Circular Normal variance. PDF means = 1 5 PDF variances = 0.5625 0.5625 Sample size = 1000 Sample mean = 1.00808 4.9792 Sample variance = 0.514381 0.555243 Sample maximum = 3.16289 7.18403 Sample minimum = -1.55877 2.31459 circular_normal_sample_test Normal end of execution. circular_normal_01_sample_test Python version: 3.6.9 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 = -0.0061213 -0.0311657 Sample variance = 1.01282 0.93777 Sample maximum = 3.07582 3.28451 Sample minimum = -3.61977 -3.4246 circular_normal_01_sample_test Normal end of execution. cosine_cdf_test Python version: 3.6.9 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 2.60439 0.130961 0.686633 2.60439 0.709922 0.0440933 0.141753 0.709922 2.46403 0.142325 0.645083 2.46403 2.11505 0.158103 0.536581 2.11505 1.71698 0.152823 0.410511 1.71698 1.61842 0.147708 0.380003 1.61842 2.96411 0.0907423 0.784195 2.96411 1.64949 0.149478 0.389563 1.64949 2.11505 0.158103 0.536581 2.11505 3.7426 -0.0272094 0.934156 3.7426 cosine_cdf_test Normal end of execution. cosine_sample_test Python version: 3.6.9 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 = 2.01969 Sample variance = 1.27971 Sample maximum = 4.84707 Sample minimum = -0.699806 cosine_sample_test Normal end of execution. coupon_sample_test Python version: 3.6.9 coupon_sample samples the coupon PDF. Number of coupon types is 5 Expected wait is about 8.04719 0 12 1 6 2 10 3 16 4 10 5 9 6 23 7 7 8 21 9 11 Average wait was 12.5 Number of coupon types is 10 Expected wait is about 23.0259 0 16 1 29 2 35 3 25 4 46 5 16 6 46 7 34 8 38 9 19 Average wait was 30.4 Number of coupon types is 15 Expected wait is about 40.6208 0 68 1 58 2 63 3 40 4 41 5 54 6 39 7 38 8 31 9 74 Average wait was 50.6 Number of coupon types is 20 Expected wait is about 59.9146 0 42 1 56 2 77 3 74 4 73 5 93 6 35 7 70 8 68 9 57 Average wait was 64.5 Number of coupon types is 25 Expected wait is about 80.4719 0 124 1 81 2 91 3 128 4 96 5 75 6 119 7 143 8 79 9 118 Average wait was 105.4 coupon_sample_test Normal end of execution. coupon_complete_pdf_test Python version: 3.6.9 coupon_complete_pdf evaluates the Coupon Complete PDF. Number of coupon types is 2 BOX_NUM PDF CDF 1 0 0 2 0.5 0.5 3 0.25 0.75 4 0.125 0.875 5 0.0625 0.9375 6 0.03125 0.96875 7 0.015625 0.984375 8 0.0078125 0.992188 9 0.00390625 0.996094 10 0.00195312 0.998047 11 0.000976562 0.999023 12 0.000488281 0.999512 13 0.000244141 0.999756 14 0.00012207 0.999878 15 6.10352e-05 0.999939 16 3.05176e-05 0.999969 17 1.52588e-05 0.999985 18 7.62939e-06 0.999992 19 3.8147e-06 0.999996 20 1.90735e-06 0.999998 Number of coupon types is 3 BOX_NUM PDF CDF 1 0 0 2 0 0 3 0.222222 0.222222 4 0.222222 0.444444 5 0.17284 0.617284 6 0.123457 0.740741 7 0.085048 0.825789 8 0.0576132 0.883402 9 0.0387136 0.922116 10 0.0259107 0.948026 11 0.0173077 0.965334 12 0.0115497 0.976884 13 0.00770358 0.984587 14 0.00513698 0.989724 15 0.00342507 0.993149 16 0.00228352 0.995433 17 0.00152239 0.996955 18 0.00101494 0.99797 19 0.000676634 0.998647 20 0.000451091 0.999098 Number of coupon types is 4 BOX_NUM PDF CDF 1 0 0 2 0 0 3 0 0 4 0.09375 0.09375 5 0.140625 0.234375 6 0.146484 0.380859 7 0.131836 0.512695 8 0.110229 0.622925 9 0.0884399 0.711365 10 0.0692368 0.780602 11 0.0533867 0.833988 12 0.040771 0.874759 13 0.0309441 0.905703 14 0.0233911 0.929094 15 0.0176349 0.946729 16 0.0132719 0.960001 17 0.00997682 0.969978 18 0.00749406 0.977472 19 0.00562627 0.983098 20 0.00422256 0.987321 coupon_complete_pdf_test: Normal end of execution. deranged_cdf_test Python version: 3.6.9 deranged_cdf evaluates the Deranged CDF deranged_cdf_inv inverts the Deranged CDF. deranged_pdf evaluates the Deranged PDF PDF parameter A = 7 X PDF CDF CDf_inv 0 0.367857 0.367857 0 1 0.368056 0.735913 1 2 0.183333 0.919246 2 3 0.0625 0.981746 3 4 0.0138889 0.995635 4 5 0.00416667 0.999802 5 6 0 0.999802 5 7 0.000198413 1 7 deranged_cdf_test Normal end of execution. deranged_sample_test Python version: 3.6.9 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 = 0.945 Sample variance = 1.01198 Sample maximum = 7 Sample minimum = 0 deranged_sample_test Normal end of execution. digamma_test: Python version: 3.6.9 digamma() computes the Digamma or Psi function. Compare the result to tabulated values. X FX FX2 (Tabulated) (DIGAMMA) DIFF 0.1 -10.42375494041108 -10.42375494041114 5.862e-14 0.2 -5.289039896592188 -5.289039896592243 5.507e-14 0.3 -3.502524222200133 -3.502524222200181 4.796e-14 0.4 -2.561384544585116 -2.561384544585158 4.174e-14 0.5 -1.963510026021423 -1.963510026021564 1.406e-13 0.6 -1.54061921389319 -1.540619213893313 1.232e-13 0.7 -1.220023553697935 -1.220023553698041 1.064e-13 0.8 -0.9650085667061385 -0.9650085667062314 9.281e-14 0.9 -0.7549269499470515 -0.7549269499471327 8.127e-14 1 -0.5772156649015329 -0.5772156649016036 7.072e-14 1.1 -0.4237549404110768 -0.4237549404111393 6.251e-14 1.2 -0.2890398965921883 -0.2890398965922431 5.479e-14 1.3 -0.1691908888667997 -0.1691908888668481 4.841e-14 1.4 -0.06138454458511615 -0.06138454458515841 4.226e-14 1.5 0.03648997397857652 0.03648997397843547 1.411e-13 1.6 0.1260474527734763 0.1260474527733536 1.227e-13 1.7 0.208547874873494 0.2085478748733869 1.071e-13 1.8 0.2849914332938615 0.2849914332937686 9.293e-14 1.9 0.3561841611640597 0.3561841611639783 8.143e-14 2 0.4227843350984671 0.4227843350983961 7.094e-14 digamma_test: Normal end of execution. dipole_cdf_test Python version: 3.6.9 dipole_cdf evaluates the Dipole CDF. dipole_cdf_inv inverts the Dipole CDF. dipole_pdf evaluates the Dipole PDF. PDF parameter A = 0 PDF parameter B = 1 X PDF CDF CDf_inv 0.7616 0.448995 0.860613 0.761719 -0.740659 0.461306 0.144836 -0.740723 0.337943 0.621215 0.70028 0.337891 1.96061 -0.0102651 0.978705 1.95898 -0.80474 0.4231 0.128833 -0.804688 -0.475606 0.587349 0.235226 -0.475586 0.472808 0.588274 0.763587 0.472656 0.762422 0.448508 0.860822 0.762695 0.0378105 0.636617 0.524048 0.0378418 -0.230446 0.632865 0.358251 -0.230469 PDF parameter A = 0.785398 PDF parameter B = 0.5 X PDF CDF CDf_inv 0.321984 0.313667 0.527052 0.322266 -4.89721 0.0122901 0.0609314 -4.88867 2.39608 0.0388537 0.862344 2.396 -0.497049 0.29789 0.289357 -0.49707 1.7199 0.0752873 0.812256 1.72021 5.56859 0.00908799 0.940955 5.57422 -2.37452 0.0393801 0.114889 -2.37402 0.587738 0.284274 0.609989 0.587891 0.562935 0.288345 0.602776 0.562988 -0.0514179 0.318306 0.40428 -0.0512695 PDF parameter A = 1.5708 PDF parameter B = 0 X PDF CDF CDf_inv -0.668595 0.219976 0.312408 -0.668945 0.324785 0.287937 0.599961 0.324707 -3.91088 0.0195342 0.0796835 -3.91211 -0.00843563 0.318287 0.497315 -0.00830078 0.380381 0.278075 0.615699 0.380371 -5.77813 0.00925676 0.0545484 -5.78516 1.54821 0.0937045 0.817452 1.54883 -1.03758 0.153286 0.24413 -1.0376 -0.0446691 0.317676 0.485791 -0.0449219 -5.68878 0.00954104 0.0553881 -5.67969 dipole_cdf_test Normal end of execution. dipole_sample_test Python version: 3.6.9 dipole_sample samples the Dipole distribution. PDF parameter A = 0 PDF parameter B = 1 Sample size = 1000 Sample mean = -0.0325717 Sample variance = 0.889366 Sample maximum = 7.40972 Sample minimum = -5.24609 PDF parameter A = 0.785398 PDF parameter B = 0.5 Sample size = 1000 Sample mean = -1.96369 Sample variance = 8957.6 Sample maximum = 497.657 Sample minimum = -2670.53 PDF parameter A = 1.5708 PDF parameter B = 0 Sample size = 1000 Sample mean = 1.06488 Sample variance = 335.776 Sample maximum = 449.563 Sample minimum = -73.4956 dipole_sample_test Normal end of execution. dirichlet_pdf_test Python version: 3.6.9 dirichlet_pdf evaluates the Dirichlet PDF. Number of components N = 3 PDF parameters A: 0: 0.25 1: 0.5 2: 1.25 PDF arguments X: 0: 0.5 1: 0.125 2: 0.375 PDF value = 0.63907 dirichlet_pdf_test Normal end of execution. dirichlet_sample_test Python version: 3.6.9 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 3.89417e-15 0.952133 0.128793 0.0360128 1 2.10338e-07 0.990679 0.251725 0.0596567 2 0.00150382 0.999923 0.619482 0.0768777 dirichlet_sample_test Normal end of execution. dirichlet_mix_pdf_test Python version: 3.6.9 dirichlet_mix_pdf evaluates the Dirichlet Mix PDF. Number of elements ELEM_NUM = 3 Number of components COMP_NUM = 2 PDF parameters A(ELEM,COMP): Col: 0 1 Row 0 : 0.25 1.5 1 : 0.5 0.5 2 : 1.25 2 Component weights: 0: 1 1: 2 PDF value = 2.12288 dirichlet_mix_pdf_test Normal end of execution. dirichlet_mix_sample_test Python version: 3.6.9 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 1.80071e-09 0.959098 0.292045 0.0577883 1 3.61811e-08 0.977618 0.162588 0.0374133 2 0.010339 0.999969 0.545368 0.0617329 dirichlet_mix_sample_test Normal end of execution. discrete_cdf_test discrete_cdf evaluates the Discrete CDF discrete_cdf_inv inverts the Discrete CDF. discrete_pdf evaluates the Discrete PDF PDF parameter A = 6 PDF parameters B: 0: 1 1: 2 2: 6 3: 2 4: 4 5: 1 X PDF CDF CDf_inv 3 0.375 0.5625 3 3 0.375 0.5625 3 3 0.375 0.5625 3 5 0.25 0.9375 5 2 0.125 0.1875 2 1 0.0625 0.0625 1 4 0.125 0.6875 4 3 0.375 0.5625 3 3 0.375 0.5625 3 5 0.25 0.9375 5 discrete_cdf_test Normal end of execution. discrete_sample_test discrete_mean computes the Discrete mean discrete_sample samples the Discrete distribution discrete_variance computes the Discrete variance. PDF parameter A = 6 PDF parameters B: 0: 1 1: 2 2: 6 3: 2 4: 4 5: 1 PDF mean = 3.5625 PDF variance = 1.74609 Sample size = 1000 Sample mean = 3.627 Sample variance = 1.77187 Sample maximum = 6 Sample minimum = 1 discrete_sample_test Normal end of execution. disk_sample_test disk_mean returns the Disk mean. disk_sample samples the Disk distribution. disk_variance returns the Disk variance. X coordinate of center is A = 10 Y coordinate of center is B = 4 Radius is C = 5 Disk mean = 10 4 Disk variance = 12.5 Sample size = 1000 Sample mean = 10.0259 4.0353 Sample variance = 12.7705 Sample maximum = 14.9429 8.89788 Sample minimum = 5.06986 -0.939182 disk_sample_test Normal end of execution. empirical_discrete_cdf_test Python version: 3.6.9 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 2 0.3 0.5 2 4.5 0.2 0.7 4.5 2 0.3 0.5 2 6 0.1 0.8 6 10 0.2 1 10 1 0.1 0.2 1 4.5 0.2 0.7 4.5 4.5 0.2 0.7 4.5 2 0.3 0.5 2 empirical_discrete_cdf_test Normal end of execution. empirical_discrete_sample_test Python version: 3.6.9 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 = 4.336 Sample variance = 11.7156 Sample maximum = 10 Sample minimum = 0 empirical_discrete_sample_test Normal end of execution. english_letter_cdf_test Python version: 3.6.9 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' 'c' 0.02782 0.12441 'c' 'w' 0.02361 0.97802 'w' 'e' 0.12702 0.29396 'e' 'e' 0.12702 0.29396 'e' 'o' 0.07507 0.68311 'o' 's' 0.06327 0.82649 's' 'h' 0.06094 0.39733 'h' 'f' 0.02228 0.31624 'f' 'i' 0.06966 0.46699 'i' english_letter_cdf_test Normal end of execution. english_sentence_length_cdf_test Python version: 3.6.9 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 41 0.00625451 0.947468 41 24 0.0253187 0.726295 24 11 0.0357028 0.303294 11 17 0.0344199 0.520808 17 2 0.0137319 0.0218106 2 6 0.0319642 0.128468 6 16 0.0354923 0.486388 16 29 0.0169393 0.825355 29 7 0.0352418 0.16371 7 20 0.0311022 0.618405 20 english_sentence_length_cdf_test Normal end of execution. english_sentence_length_sample_test Python version: 3.6.9 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 = 18.809 Sample variance = 151.747 Sample maximum = 67 Sample minimum = 1 english_sentence_length_sample_test Normal end of execution. english_word_length_cdf_test Python version: 3.6.9 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 2 0.169755 0.201356 2 3 0.211926 0.413282 3 10 0.0276608 0.965289 10 3 0.211926 0.413282 3 3 0.211926 0.413282 3 8 0.0562317 0.897307 8 2 0.169755 0.201356 2 2 0.169755 0.201356 2 4 0.156785 0.570067 4 2 0.169755 0.201356 2 english_word_length_cdf_test Normal end of execution. english_word_length_sample_test Python version: 3.6.9 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 = 4.732 Sample variance = 7.40818 Sample maximum = 17 Sample minimum = 1 english_word_length_sample_test Normal end of execution. erlang_cdf_test Python version: 3.6.9 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 10.5347 0.0483119 0.854338 10.5352 5.51021 0.13332 0.392022 5.50977 4.37774 0.131724 0.239841 4.37793 8.60459 0.0806707 0.731474 8.60547 11.3147 0.0382813 0.88799 11.3125 1.63995 0.018587 0.00430353 1.64062 8.84982 0.0760384 0.750686 8.84961 6.16357 0.126045 0.476988 6.16406 6.74447 0.116677 0.547585 6.74414 5.80754 0.130551 0.431276 5.80762 erlang_cdf_test Normal end of execution. erlang_sample_test Python version: 3.6.9 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 = 6.95935 Sample variance = 11.3081 Sample maximum = 21.6682 Sample minimum = 1.20483 erlang_sample_test Normal end of execution. exponential_cdf_test Python version: 3.6.9 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 2.71025 0.212615 0.574771 2.71025 6.01277 0.0407813 0.918437 6.01277 4.22222 0.099833 0.800334 4.22222 1.16493 0.460423 0.0791548 1.16493 5.88702 0.0434278 0.913144 5.88702 2.6945 0.214296 0.571408 2.6945 2.92525 0.190944 0.618111 2.92525 1.75335 0.343069 0.313861 1.75335 2.15443 0.280729 0.438541 2.15443 2.72136 0.211437 0.577125 2.72136 exponential_cdf_test Normal end of execution. exponential_sample_test Python version: 3.6.9 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 = 10.7797 Sample variance = 93.0992 Sample maximum = 72.2107 Sample minimum = 1.00687 exponential_sample_test Normal end of execution. exponential_01_cdf_test Python version: 3.6.9 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 0.683945 0.504622 0.495378 0.683945 1.28567 0.276465 0.723535 1.28567 3.04878 0.0474167 0.952583 3.04878 2.01583 0.133209 0.866791 2.01583 1.01936 0.360825 0.639175 1.01936 0.453026 0.635701 0.364299 0.453026 0.884256 0.413021 0.586979 0.884256 1.14479 0.318291 0.681709 1.14479 0.564214 0.568807 0.431193 0.564214 0.955692 0.384546 0.615454 0.955692 exponential_01_sample_test Normal end of execution. exponential_01_sample_test Python version: 3.6.9 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 = 0.999195 Sample variance = 0.928826 Sample maximum = 5.97702 Sample minimum = 5.71488e-05 exponential_01_sample_test Normal end of execution. extreme_values_cdf_test Python version: 3.6.9 extreme_values_cdf evaluates the Extreme Values CDF extreme_values_cdf_inv inverts the Extreme Values CDF. extreme_values_pdf evaluates the Extreme Values PDF PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDf_inv -0.381307 0.0807369 0.109512 -0.381307 1.78111 0.122292 0.341062 1.78111 6.93434 0.0530539 0.824436 6.93434 3.44699 0.110993 0.539375 3.44699 -1.18432 0.0535197 0.0555465 -1.18432 0.156198 0.0970111 0.157407 0.156198 1.32507 0.119322 0.285849 1.32507 10.5606 0.0181374 0.943989 10.5606 7.6189 0.0439261 0.857558 7.6189 -0.247354 0.0850405 0.120617 -0.247354 extreme_values_cdf_test Normal end of execution. extreme_values_sample_test Python version: 3.6.9 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 = 3.84249 Sample variance = 16.8278 Sample maximum = 21.1807 Sample minimum = -5.15042 extreme_values_sample_test Normal end of execution. f_cdf_test Python version: 3.6.9 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 484.173 1 1 2.98163e-05 0.0289122 171.577 1 1 0.000140811 0.0485074 0.766524 1 1 0.205811 0.542194 1.59444 1 1 0.0971631 0.426415 0.294719 1 1 0.452867 0.68337 3046.55 1 1 1.89232e-06 0.0115326 2.61343 1 1 0.0544911 0.352667 1.60064 1 1 0.0967439 0.425814 0.1262 1 1 0.795619 0.782696 0.791081 1 1 0.199813 0.537214 f_cdf_test Normal end of execution. f_sample_test Python version: 3.6.9 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 = 1.49842 Sample variance = 2.90388 Sample maximum = 24.7283 Sample minimum = 0.111008 f_sample_test Normal end of execution. fermi_dirac_sample_test Python version: 3.6.9 fermi_dirac_sample samples the Fermi Dirac distribution. U = 1 V = 1 SAMPLE_NUM = 10000 Sample mean = 0.600786 Sample variance = 0.178257 Maximum value = 2.71249 Minimum value = 0.000355381 U = 2 V = 1 SAMPLE_NUM = 10000 Sample mean = 1.04608 Sample variance = 0.437344 Maximum value = 3.54897 Minimum value = 0.000101515 U = 4 V = 1 SAMPLE_NUM = 10000 Sample mean = 2.02422 Sample variance = 1.41821 Maximum value = 5.25467 Minimum value = 0.000106975 U = 8 V = 1 SAMPLE_NUM = 10000 Sample mean = 3.9926 Sample variance = 5.44033 Maximum value = 9.52331 Minimum value = 0.000168473 U = 16 V = 1 SAMPLE_NUM = 10000 Sample mean = 8.00149 Sample variance = 21.1067 Maximum value = 17.2859 Minimum value = 0.00068667 U = 32 V = 1 SAMPLE_NUM = 10000 Sample mean = 15.8706 Sample variance = 85.2449 Maximum value = 32.8182 Minimum value = 0.00313556 U = 1 V = 0.25 SAMPLE_NUM = 10000 Sample mean = 0.510948 Sample variance = 0.0915761 Maximum value = 1.4043 Minimum value = 1.63291e-05 fermi_dirac_sample_test Normal end of execution. fisher_pdf_test Python version: 3.6.9 fisher_pdf evaluates the Fisher PDF. PDF Input: Concentration parameter KAPPA = 0 1 0 0 X PDF 0.600743 -0.0639933 0.796877 0.0795775 -0.629584 -0.765092 0.135121 0.0795775 0.37298 0.883063 0.284754 0.0795775 0.555421 0.606622 -0.568786 0.0795775 -0.556761 0.13853 0.81904 0.0795775 -0.188716 -0.747668 0.636694 0.0795775 0.961217 0.0979336 -0.257821 0.0795775 0.453777 0.727063 0.515234 0.0795775 -0.568319 0.0842044 -0.818488 0.0795775 0.0887255 -0.972778 -0.214081 0.0795775 PDF Input: Concentration parameter KAPPA = 0.5 1 0 0 X PDF -0.929927 -0.141855 -0.339282 0.0479636 0.513035 -0.801003 0.308526 0.0986841 0.613313 -0.409569 -0.675352 0.103758 0.78561 0.0931131 0.611675 0.113093 0.625291 -0.777013 0.0725397 0.104381 -0.606462 -0.141936 -0.782341 0.0563834 -0.0569088 0.209792 -0.976088 0.0742139 0.170207 0.00824627 -0.985374 0.0831387 -0.0786483 -0.993025 -0.0878408 0.0734116 -0.0969945 -0.990921 -0.093104 0.0727413 PDF Input: Concentration parameter KAPPA = 10 1 0 0 X PDF 0.867802 0.494498 -0.0489033 0.424319 0.934033 -0.0896427 0.345754 0.822869 0.774618 -0.519829 -0.3602 0.167108 0.955536 -0.184637 -0.229911 1.02028 0.850388 -0.417128 0.320694 0.356503 0.907488 0.300162 -0.293885 0.631023 0.945858 -0.283638 -0.157802 0.92616 0.941368 -0.249226 -0.227404 0.885494 0.920404 0.361312 0.149368 0.718023 0.858003 -0.0929899 0.505158 0.38471 fisher_pdf_test Normal end of execution. fisk_cdf_test Python version: 3.6.9 fisk_cdf evaluates the Fisk CDF fisk_cdf_inv inverts the Fisk CDF. fisk_pdf evaluates the Fisk PDF PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDf_inv 2.23572 0.374911 0.190854 2.23572 2.21546 0.36951 0.183311 2.21546 1.66745 0.155299 0.0358357 1.66745 2.17149 0.356817 0.167337 2.17149 3.52409 0.263676 0.667788 3.52409 5.17473 0.0641338 0.90094 5.17473 2.44106 0.412454 0.272237 2.44106 2.50176 0.417448 0.29744 2.50176 2.28818 0.387518 0.210859 2.28818 2.03492 0.309839 0.121696 2.03492 fisk_cdf_test Normal end of execution. fisk_sample_test Python version: 3.6.9 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 = 3.39895 Sample variance = 4.00405 Sample maximum = 30.1019 Sample minimum = 1.16187 fisk_sample_test Normal end of execution. folded_normal_cdf_test Python version: 3.6.9 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 1.1756 0.203994 0.246828 1.17563 3.77605 0.132441 0.695988 3.77555 9.62031 0.00535456 0.994405 9.63212 3.31909 0.148344 0.63181 3.31851 3.63804 0.137307 0.677374 3.63823 4.79982 0.0962211 0.812954 4.8002 2.90412 0.162032 0.56738 2.90372 4.54102 0.105242 0.786889 4.54105 2.21792 0.182123 0.449088 2.21773 1.25287 0.202794 0.262546 1.25308 folded_normal_cdf_test Normal end of execution. folded_normal_sample_test Python version: 3.6.9 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 = 3.0554 Sample variance = 4.66101 Sample maximum = 11.5287 Sample minimum = 0.000977054 folded_normal_sample_test Normal end of execution. frechet_cdf_test Python version: 3.6.9 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 1.33157 0.624762 0.654719 1.33157 1.08392 0.991068 0.456003 1.08392 0.765442 0.939916 0.107552 0.765442 0.761767 0.92761 0.104119 0.761767 1.1289 0.921781 0.499039 1.1289 2.7513 0.0499015 0.953119 2.7513 0.839578 1.11439 0.18457 0.839578 0.767899 0.947954 0.109871 0.767899 2.0407 0.153781 0.88899 2.0407 0.866851 1.14449 0.215411 0.866851 frechet_cdf_test Normal end of execution. frechet_sample_test Python version: 3.6.9 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 = 1.35842 Sample variance = 0.60341 Sample maximum = 8.56107 Sample minimum = 0.519673 frechet_sample_test Normal end of execution. gamma_cdf_test Python version: 3.6.9 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 6.80009 0.104296 0.741711 13.6672 0.00511122 0.990302 6.392 0.118318 0.696307 2.36577 0.111178 0.0645988 8.78602 0.0500085 0.890516 8.35964 0.0593711 0.867242 2.1892 0.094819 0.0463925 5.73214 0.141487 0.610575 4.46539 0.17655 0.40668 3.32014 0.169815 0.202979 gamma_cdf_test Normal end of execution. gamma_sample_test Python version: 3.6.9 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 = 7.16087 Sample variance = 18.7814 Sample maximum = 36.793 Sample minimum = 1.20752 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 = 2.26462 Sample variance = 0.130076 Sample maximum = 5.46348 Sample minimum = 2 gamma_sample_test Normal end of execution. gamma_inc_values_test: Python version: 3.6.9 gamma_inc_values stores values of the incomplete Gamma function. A X gamma_inc(A,X) 0.100000 0.030000 2.49030283630057 0.100000 0.300000 0.8718369702247978 0.100000 1.500000 0.1079213896175866 0.500000 0.075000 1.238121685818417 0.500000 0.750000 0.3911298052193973 0.500000 3.500000 0.01444722098952533 1.000000 0.100000 0.9048374180359596 1.000000 1.000000 0.3678794411714423 1.000000 5.000000 0.006737946999085467 1.100000 0.100000 0.8827966752611692 1.100000 1.000000 0.3908330082003269 1.100000 5.000000 0.008051456628620992 2.000000 0.150000 0.9898141728888165 2.000000 1.500000 0.5578254003710746 2.000000 7.000000 0.00729505572443613 6.000000 2.500000 114.9574754165633 6.000000 12.000000 2.440923530031405 11.000000 16.000000 280854.6620274718 26.000000 25.000000 8.576480283455533e+24 41.000000 45.000000 2.085031346403364e+47 gamma_inc_values_test: Normal end of execution. geometric_cdf_test Python version: 3.6.9 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 1 0.25 0.25 2 1 0.25 0.25 2 3 0.140625 0.578125 4 4 0.105469 0.683594 5 1 0.25 0.25 2 3 0.140625 0.578125 4 9 0.0250282 0.924915 10 2 0.1875 0.4375 3 8 0.033371 0.899887 9 geometric_cdf_test Normal end of execution. geometric_sample_test Python version: 3.6.9 geometric_mean computes the Geometric mean geometric_sample samples the Geometric distribution geometric_variance computes the Geometric variance. PDF parameter A = 0.25 PDF mean = 4 PDF variance = 12 Sample size = 1000 Sample mean = 4.055 Sample variance = 12.146 Sample maximum = 24 Sample minimum = 1 geometric_sample_test Normal end of execution. gompertz_cdf_test Python version: 3.6.9 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 0.347512 1.1743 0.692357 0.347512 0.21791 1.72284 0.506228 0.21791 0.127809 2.19521 0.3303 0.127809 1.31495 0.0119161 0.998403 1.31495 0.185379 1.88449 0.447581 0.185379 0.416053 0.94199 0.764668 0.416053 0.178084 1.92212 0.433696 0.178084 1.02769 0.0682291 0.988845 1.02769 0.71307 0.309122 0.937143 0.71307 0.0634324 2.58064 0.176789 0.0634324 gompertz_cdf_test Normal end of execution. gompertz_sample_test Python version: 3.6.9 gompertz_sample samples the Gompertz distribution PDF parameter A = 2 PDF parameter B = 3 Sample size = 1000 Sample mean = 0.267505 Sample variance = 0.0526379 Sample maximum = 1.37066 Sample minimum = 2.97328e-06 gompertz_sample_test Normal end of execution. gumbel_cdf_test Python version: 3.6.9 gumbel_cdf evaluates the Gumbel CDF. gumbel_cdf_inv inverts the Gumbel CDF. gumbel_pdf evaluates the Gumbel PDF. X PDF CDF CDf_inv 0.815052 0.284316 0.642354 0.815052 0.67327 0.306264 0.600473 0.67327 -0.211777 0.359121 0.290581 -0.211777 -0.21701 0.358672 0.288703 -0.21701 -0.800965 0.240094 0.107777 -0.800965 0.83051 0.281862 0.64673 0.83051 -1.00034 0.179268 0.0659263 -1.00034 -0.388554 0.337465 0.228814 -0.388554 0.00578346 0.367873 0.370007 0.00578346 0.432146 0.339168 0.522508 0.432146 gumbel_cdf_test Normal end of execution. gumbel_sample_test Python version: 3.6.9 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 = 0.633054 Sample variance = 1.82666 Sample maximum = 6.50115 Sample minimum = -1.80374 gumbel_sample_test Normal end of execution. half_normal_cdf_test Python version: 3.6.9 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 1.11843 0.341195 0.423986 1.11843 1.06358 0.346338 0.405129 1.06358 0.599845 0.381397 0.235764 0.599845 1.09818 0.343115 0.417057 1.09818 0.491143 0.387093 0.193986 0.491143 4.75436 0.0236491 0.982554 4.75436 1.29948 0.323027 0.484141 1.29948 0.318428 0.393918 0.1265 0.318428 1.80941 0.264958 0.634377 1.80941 0.349683 0.392891 0.138796 0.349683 half_normal_cdf_test Normal end of execution. half_normal_sample_test Python version: 3.6.9 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 = 7.99011 Sample variance = 33.3258 Sample maximum = 29.8792 Sample minimum = 0.0033248 half_normal_sample_test Normal end of execution. hypergeometric_cdf_test Python version: 3.6.9 hypergeometric_cdf evaluates the Hypergeometric CDF. hypergeometric_pdf evaluates the Hypergeometric PDF. PDF argument X = 7 Total number of balls = 100 Number of white balls = 7 Number of balls taken = 10 PDF value = = 7.49646e-09 CDF value = = 1 hypergeometric_cdf_test Normal end of execution. hypergeometric_sample_test Python version: 3.6.9 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 = 0.714 Sample variance = 0.570204 Sample maximum = 4 Sample minimum = 0 hypergeometric_sample_test Normal end of execution. i4_factorial_log_test Python version: 3.6.9 i4_factorial_log evaluates the 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_factorial_log_test: Normal end of execution. i4_is_power_of_10_test Python version: 3.6.9 i4_is_power_of_10 reports whether an I4 is a power of 10. I i4_is_power_of_10(I) 97 False 98 False 99 False 100 True 101 False 102 False 103 False i4_is_power_of_10_test: Normal end of execution. i4mat_print_test: Python version: 3.6.9 Test i4mat_print, which 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_test: Normal end of execution. i4mat_print_some_test Python version: 3.6.9 i4mat_print_some prints some of an I4MAT. Here is I4MAT, rows 0:2, cols 3:5: Col: 3 4 5 Row 0: 14 15 16 1: 24 25 26 2: 34 35 36 i4mat_print_some_test: Normal end of execution. i4row_max_test Python version: 3.6.9 i4row_max computes maximums of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 Row maximums: 0 4 1 8 2 12 i4row_max_test: Normal end of execution. i4row_mean_test Python version: 3.6.9 i4row_mean computes row means of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 The row means: 0: 2.5 1: 6.5 2: 10.5 i4row_mean_test: Normal end of execution. i4row_min_test Python version: 3.6.9 i4row_min computes minimums of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 Row minimums: 0 1 1 5 2 9 i4row_min_test: Normal end of execution. i4row_variance_test Python version: 3.6.9 i4row_variance computes variances of an I4ROW. The matrix: Col: 0 1 2 3 Row 0: 1 2 3 4 1: 5 6 7 8 2: 9 10 11 12 The row variances: 0: 1.66667 1: 1.66667 2: 1.66667 i4row_variance_test: Normal end of execution. i4vec_print_test Python version: 3.6.9 i4vec_print prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 i4vec_print_test: Normal end of execution. i4vec_run_count_test Python version: 3.6.9 i4vec_run_count counts runs in an I4VEC Run Count Sequence 13 1 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 1 11 1 0 1 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 15 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 1 0 10 1 0 1 1 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 0 14 0 1 0 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 0 1 10 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 10 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 0 0 0 9 1 1 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 11 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 0 1 0 1 0 13 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 i4vec_run_count_test: Normal end of execution. i4vec_unique_count_test Python version: 3.6.9 i4vec_unique_count counts unique entries in an I4VEC. Input vector: 0 20 1 14 2 5 3 15 4 2 5 13 6 20 7 15 8 15 9 19 10 12 11 16 12 4 13 9 14 8 15 8 16 17 17 6 18 5 19 5 Number of unique entries is 14 i4vec_unique_count_test: Normal end of execution. inverse_gaussian_cdf_test Python version: 3.6.9 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 1.40906 0.233913 0.337122 14.7125 0.00773594 0.925595 0.929236 0.308634 0.2073 1.42148 0.232174 0.340017 10.5399 0.0146752 0.880929 0.42538 0.284205 0.0443691 2.83419 0.11067 0.567293 1.4339 0.230451 0.34289 2.10057 0.157905 0.470293 3.77341 0.0757525 0.653284 inverse_gaussian_cdf_test Normal end of execution. inverse_gaussian_sample_test Python version: 3.6.9 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 = 2.02382 Sample variance = 2.60071 Sample maximum = 11.627 Sample minimum = 0.22052 inverse_gaussian_sample_test Normal end of execution. laplace_cdf_test Python version: 3.6.9 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 -1.27751 0.0800544 0.160109 -1.27751 -0.213461 0.136283 0.272565 -0.213461 1.99718 0.151847 0.696306 1.99718 0.874594 0.234806 0.469611 0.874594 -1.99472 0.0559301 0.11186 -1.99472 0.1804 0.165946 0.331892 0.1804 3.70599 0.0646162 0.870768 3.70599 3.61616 0.0675847 0.864831 3.61616 6.21578 0.0184224 0.963155 6.21578 0.0399148 0.154689 0.309379 0.0399148 laplace_cdf_test Normal end of execution. laplace_sample_test Python version: 3.6.9 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 = 1.16883 Sample variance = 7.77822 Sample maximum = 13.8301 Sample minimum = -10.4591 laplace_sample_test Normal end of execution. levy_cdf_test Python version: 3.6.9 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 338.766 9.06182e-05 0.938664 338.766 1598.87 8.82761e-06 0.971778 1598.87 26.2522 0.00427345 0.778383 26.2522 1.97922 0.209698 0.152963 1.97922 5.01723 0.0546294 0.480444 5.01723 52.0259 0.00151785 0.843061 52.0259 4.25347 0.0706999 0.433013 4.25347 11.11 0.0158979 0.656484 11.11 2.84191 0.131141 0.297397 2.84191 5.35677 0.0493168 0.498066 5.35677 levy_cdf_test Normal end of execution. log_normal_cdf_test Python version: 3.6.9 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 65916.9 2.38887e-06 0.686934 65916.9 72657.8 2.12004e-06 0.7021 72657.8 7997.45 2.00332e-05 0.326256 7997.45 735702 7.14503e-08 0.940545 735702 494099 1.38011e-07 0.916582 494099 4976.28 2.86356e-05 0.254262 4976.28 1.53112e+06 1.95907e-08 0.970293 1.53112e+06 1.31095e+06 2.59972e-08 0.965324 1.31095e+06 1.35329e+06 2.45437e-08 0.966393 1.35329e+06 12341.1 1.38989e-05 0.398407 12341.1 log_normal_cdf_test Normal end of execution. log_normal_sample_test Python version: 3.6.9 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 = 19.1937 Sample variance = 7064.74 Sample maximum = 1351.8 Sample minimum = 0.0016519 log_normal_sample_test Normal end of execution. log_series_cdf_test Python version: 3.6.9 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_cdf_test Normal end of execution. log_series_sample_test Python version: 3.6.9 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 = 1.145 Sample variance = 0.179975 Sample maximum = 6 Sample minimum = 1 log_series_sample_test Normal end of execution. log_uniform_cdf_test Python version: 3.6.9 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 14.7924 0.0293593 0.869009 14.7924 9.41255 0.0461399 0.672677 9.41255 2.74944 0.157957 0.138215 2.74944 5.08432 0.0854184 0.405203 5.08432 18.4372 0.0235553 0.964665 18.4372 6.68597 0.0649561 0.524134 6.68597 9.5736 0.0453638 0.680045 9.5736 2.13894 0.203041 0.0291696 2.13894 5.3665 0.0809269 0.428661 5.3665 16.978 0.0255798 0.928857 16.978 log_uniform_cdf_test Normal end of execution. log_uniform_sample_test Python version: 3.6.9 log_uniform_mean computes the Log Uniform mean log_uniform_sample samples the Log Uniform distribution log_uniform_variance computes the Log Uniform variance PDF parameter A = 2 PDF parameter B = 20 PDF mean = 7.8173 PDF variance = 24.8801 Sample size = 1000 Sample mean = 7.84705 Sample variance = 25.899 Sample maximum = 19.9965 Sample minimum = 2.00565 log_uniform_sample_test Normal end of execution. logistic_cdf_test Python version: 3.6.9 logistic_cdf evaluates the Logistic CDF logistic_cdf_inv inverts the Logistic CDF. logistic_pdf evaluates the Logistic PDF PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDf_inv -1.34673 0.0902172 0.236247 -1.34673 6.28742 0.0309859 0.933622 6.28742 1.78904 0.120259 0.597371 1.78904 0.901304 0.124924 0.487666 0.901304 6.43927 0.0290011 0.938175 6.43927 4.63639 0.0600742 0.860349 4.63639 -1.88193 0.0773818 0.191396 -1.88193 8.35534 0.0120252 0.975342 8.35534 1.02669 0.124994 0.503336 1.02669 -1.32528 0.0907272 0.238188 -1.32528 logistic_cdf_test Normal end of execution. logistic_sample_test Python version: 3.6.9 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 = 1.81463 Sample variance = 29.8548 Sample maximum = 35.6563 Sample minimum = -17.336 logistic_sample_test Normal end of execution. lorentz_cdf_test Python version: 3.6.9 lorentz_cdf evaluates the Lorentz CDF lorentz_cdf_inv inverts the Lorentz CDF. lorentz_pdf evaluates the Lorentz PDF X PDF CDF CDf_inv -0.575656 0.239083 0.333738 -0.575656 -0.125746 0.313355 0.460183 -0.125746 -1.77677 0.0765734 0.163175 -1.77677 -2.01315 0.062997 0.146751 -2.01315 -0.754654 0.202809 0.294221 -0.754654 3.97124 0.0189801 0.921479 3.97124 0.999621 0.159215 0.74994 0.999621 0.111963 0.314369 0.535491 0.111963 -1.62855 0.0871566 0.175288 -1.62855 0.326385 0.287666 0.600422 0.326385 lorentz_cdf_test Normal end of execution. lorentz_sample_test Python version: 3.6.9 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 = -8.40595 Sample variance = 56690.4 Sample maximum = 108.743 Sample minimum = -7484.75 lorentz_sample_test Normal end of execution. maxwell_cdf_test Python version: 3.6.9 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 2.52737 0.286699 0.529636 2.52734 3.56731 0.258639 0.687863 3.56738 4.46042 0.165024 0.784152 4.46094 3.81736 0.235123 0.718127 3.81738 5.5467 0.0655747 0.864128 5.54688 3.38267 0.27302 0.663699 3.38281 0.946966 0.0799535 0.185918 0.947266 3.97994 0.218124 0.736362 3.98047 3.93769 0.222636 0.731728 3.9375 2.34203 0.275592 0.495483 2.3418 maxwell_cdf_test Normal end of execution. maxwell_sample_test Python version: 3.6.9 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 = 3.16735 Sample variance = 1.83048 Sample maximum = 8.5477 Sample minimum = 0.242292 maxwell_sample_test Normal end of execution. multinomial_coef_test Python version: 3.6.9 multinomial_coef1 computes multinomial coefficients using the Gamma function multinomial_coef2 computes multinomial coefficients directly. Line 10 of the BINOMIAL table: 0 10 1 1 1 9 10 10 2 8 45 45 3 7 120 120 4 6 210 210 5 5 252 252 6 4 210 210 7 3 120 120 8 2 45 45 9 1 10 10 10 0 1 1 Level 5 of the TRINOMIAL coefficients: 0 0 5 1 1 0 1 4 5 5 0 2 3 10 10 0 3 2 10 10 0 4 1 5 5 0 5 0 1 1 1 0 4 5 5 1 1 3 20 20 1 2 2 30 30 1 3 1 20 20 1 4 0 5 5 2 0 3 10 10 2 1 2 30 30 2 2 1 30 30 2 3 0 10 10 3 0 2 10 10 3 1 1 20 20 3 2 0 10 10 4 0 1 5 5 4 1 0 5 5 5 0 0 1 1 multinomial_coef_test Normal end of execution. multinomial_pdf_test Python version: 3.6.9 multinomial_pdf evaluates the Multinomial PDF. PDF argument X: 0 0 1 2 2 3 PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 0: 0.1 1: 0.5 2: 0.4 PDF value = 0.16 multinomial_pdf_test Normal end of execution. multinomial_sample_test Python version: 3.6.9 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 0.625 0.54492 1 0 5 2.472 1.2825 2 0 5 1.903 1.2068 multinomial_sample_test Normal end of execution. multinoulli_pdf_test Python version: 3.6.9 multinoulli_pdf evaluates the Multinoulli PDF. X pdf(X) -1 0 0 0.283639 1 0.0925249 2 0.0706549 3 0.288182 4 0.264999 5 0 multinoulli_pdf_test Normal end of execution. nakagami_cdf_test Python version: 3.6.9 nakagami_cdf evaluates the Nakagami CDF nakagami_pdf evaluates the Nakagami PDF X PDF CDF CDf_inv 3.18257 0.586699 0.692394 3.18258 3.2582 0.540746 0.735053 3.2582 3.31623 0.503068 0.765346 3.31623 3.36515 0.470346 0.789159 3.36515 3.40825 0.441184 0.808803 3.40825 3.44721 0.414809 0.82548 3.44721 3.48305 0.390724 0.839911 3.48305 3.5164 0.36858 0.852572 3.5164 3.54772 0.348118 0.863796 3.54772 3.57735 0.329135 0.873828 3.57735 nakagami_cdf_test Normal end of execution. nakagami_sample_test Python version: 3.6.9 nakagami_mean computes the Nakagami mean nakagami_variance computes the Nakagami variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 2.91874 PDF variance = 0.318446 nakagami_sample_test Normal end of execution. negative_binomial_cdf_test Python version: 3.6.9 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 8 0.0778656 0.632919 8 8 0.0778656 0.632919 8 7 0.0889893 0.555054 7 5 0.105469 0.367188 5 23 0.00327031 0.988405 23 3 0.09375 0.15625 3 3 0.09375 0.15625 3 7 0.0889893 0.555054 7 16 0.0167043 0.936524 16 8 0.0778656 0.632919 8 negative_binomial_cdf_test Normal end of execution. negative_binomial_sample_test Python version: 3.6.9 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 = 2.669 Sample variance = 0.867439 Sample maximum = 8 Sample minimum = 2 negative_binomial_sample_test Normal end of execution. normal_01_cdf_test Python version: 3.6.9 normal_01_cdf evaluates the Normal 01 CDF normal_01_cdf_inv inverts the Normal 01 CDF. normal_01_pdf evaluates the Normal 01 PDF X PDF CDF CDf_inv -1.93939 0.0608375 0.0262271 -1.93939 -0.801237 0.289405 0.211497 -0.801237 0.132326 0.395465 0.552637 0.132326 0.55251 0.34247 0.709701 0.55251 1.952 0.0593624 0.974531 1.952 -2.84401 0.00699098 0.00222748 -2.84401 -0.659817 0.320903 0.254686 -0.659817 0.16505 0.393545 0.565548 0.16505 -1.9624 0.0581668 0.0248581 -1.9624 1.15172 0.205529 0.875282 1.15172 normal_01_cdf_test Normal end of execution. normal_01_cdf_values_test: Python version: 3.6.9 normal_01_cdf_values stores values of the unit normal CDF. X normal_01_cdf(X) 0.000000 0.5000000000000000 0.100000 0.5398278372770290 0.200000 0.5792597094391030 0.300000 0.6179114221889526 0.400000 0.6554217416103242 0.500000 0.6914624612740131 0.600000 0.7257468822499270 0.700000 0.7580363477769270 0.800000 0.7881446014166033 0.900000 0.8159398746532405 1.000000 0.8413447460685429 1.500000 0.9331927987311419 2.000000 0.9772498680518208 2.500000 0.9937903346742240 3.000000 0.9986501019683699 3.500000 0.9997673709209645 4.000000 0.9999683287581669 normal_01_cdf_values_test: Normal end of execution. normal_01_sample_test Python version: 3.6.9 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 = 0.0202395 Sample variance = 0.969186 Sample maximum = 3.08783 Sample minimum = -3.20867 normal_01_sample_test Normal end of execution. normal_cdf_test Python version: 3.6.9 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 87.1325 0.0184088 0.195492 87.1325 102.781 0.0261431 0.57353 102.781 96.6655 0.025947 0.41204 96.6655 87.6529 0.0189535 0.205214 87.6529 97.9292 0.0263439 0.445098 97.9292 95.1305 0.025231 0.372729 95.1305 113.277 0.0179764 0.811951 113.277 98.1902 0.0264033 0.451984 98.1902 88.6562 0.0199815 0.224748 88.6562 107.975 0.0230908 0.70252 107.975 normal_cdf_test Normal end of execution. normal_sample_test Python version: 3.6.9 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 = 100.192 Sample variance = 218.352 Sample maximum = 149.35 Sample minimum = 50.9934 normal_sample_test Normal end of execution. normal_truncated_ab_cdf_test Python version: 3.6.9 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 97.5522 0.0166384 0.459142 97.5522 83.9083 0.0135903 0.24845 83.9083 96.3442 0.0165406 0.439098 96.3442 127.019 0.00932295 0.877265 127.019 93.4677 0.0161573 0.392021 93.4677 83.7521 0.0135355 0.246331 83.7521 113.623 0.0144118 0.716962 113.623 84.0306 0.013633 0.250114 84.0306 117.536 0.0130725 0.770802 117.536 87.9678 0.01489 0.306345 87.9678 normal_truncated_ab_cdf_test Normal end of execution. normal_truncated_ab_sample_test Python version: 3.6.9 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 = 99.6594 Sample variance = 479.644 Sample maximum = 149.966 Sample minimum = 50.442 normal_truncated_ab_sample_test Normal end of execution. normal_truncated_a_cdf_test Python version: 3.6.9 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 140.194 0.00448403 0.944799 140.194 107.179 0.0156697 0.603991 107.179 95.0761 0.0160155 0.408474 95.0761 93.4644 0.0157806 0.382843 93.4644 122.038 0.011072 0.80658 122.038 124.25 0.010201 0.830116 124.25 77.9289 0.011059 0.169773 77.9289 74.0326 0.00952108 0.129673 74.0326 67.087 0.00686434 0.0729081 67.087 96.6953 0.0161871 0.434554 96.6953 normal_truncated_a_cdf_test Normal end of execution. normal_truncated_a_sample_test Python version: 3.6.9 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 = 101.025 Sample variance = 540.355 Sample maximum = 180.031 Sample minimum = 50.5508 normal_truncated_a_sample_test Normal end of execution. normal_truncated_b_cdf_test Python version: 3.6.9 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 91.1391 0.0153351 0.369922 91.1391 112.441 0.0144274 0.706709 112.441 107.301 0.0156475 0.629182 107.301 113.398 0.0141449 0.720379 113.398 123.174 0.0106261 0.842189 123.174 69.6082 0.00779922 0.114663 69.6082 119.928 0.0118848 0.805635 119.928 90.2129 0.0151246 0.355814 90.2129 62.8116 0.00540092 0.0700296 62.8116 116.095 0.0132727 0.757381 116.095 normal_truncated_b_cdf_test Normal end of execution. normal_truncated_b_sample_test Python version: 3.6.9 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 = 98.3858 Sample variance = 515.051 Sample maximum = 149.388 Sample minimum = 13.9709 normal_truncated_b_sample_test Normal end of execution. owen_values_test: Python version: 3.6.9 owen_values stores values of the OWEN function. H A T 0.062500 0.250000 0.038912 6.500000 0.437500 0.000000 7.000000 0.968750 0.000000 4.781250 0.062500 0.000000 2.000000 0.500000 0.008625 1.000000 0.999997 0.066742 1.000000 0.500000 0.043065 1.000000 1.000000 0.066742 1.000000 2.000000 0.078468 1.000000 3.000000 0.079300 0.500000 0.500000 0.064489 0.500000 1.000000 0.106671 0.500000 2.000000 0.141581 0.500000 3.000000 0.151084 0.250000 0.500000 0.071347 0.250000 1.000000 0.120129 0.250000 2.000000 0.166613 0.250000 3.000000 0.184750 0.125000 0.500000 0.073173 0.125000 1.000000 0.123763 0.125000 2.000000 0.173744 0.125000 3.000000 0.195119 0.007812 0.500000 0.073789 0.007812 1.000000 0.124995 0.007812 2.000000 0.176198 0.007812 3.000000 0.198777 0.007812 10.000000 0.234089 0.007812 100.000000 0.247946 owen_values_test: Normal end of execution. pareto_cdf_test Python version: 3.6.9 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 0.643974 2.19083 0.717832 0.643974 0.765045 0.779285 0.880762 0.765045 0.713439 1.18489 0.830931 0.713439 0.657388 1.93593 0.745468 0.657388 0.7618 0.79942 0.8782 0.7618 0.644356 2.18306 0.718667 0.644356 0.502391 9.71788 0.0235661 0.502391 0.618392 2.79408 0.654433 0.618392 0.617853 2.80872 0.652925 0.617853 0.705769 1.26429 0.821541 0.705769 pareto_cdf_test Normal end of execution. pareto_sample_test Python version: 3.6.9 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 = 0.619695 Sample variance = 0.0198291 Sample maximum = 1.90338 Sample minimum = 0.500289 pareto_sample_test Normal end of execution. pearson_05_pdf_test Python version: 3.6.9 pearson_05_pdf evaluates the Pearson 05 PDF. PDF argument X = 5 PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF value = 0.0758163 pearson_05_pdf_test Normal end of execution. planck_pdf_test Python version: 3.6.9 planck_pdf evaluates the Planck PDF. PDF parameter A = 2 PDF parameter B = 3 X PDF 2.7041 0.21922 1.7624 0.409364 0.595859 0.227347 0.20664 0.0424799 1.52466 0.434424 1.79241 0.404832 0.633885 0.245814 3.70707 0.0756916 1.0064 0.387316 3.24909 0.127476 planck_pdf_test Normal end of execution. planck_sample_test Python version: 3.6.9 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 = 1.95125 Sample variance = 1.10389 Sample maximum = 6.85112 Sample minimum = 0.0913896 planck_sample_test Normal end of execution. poisson_cdf_test Python version: 3.6.9 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 10 0.12511 0.58304 10 10 0.12511 0.58304 10 15 0.0347181 0.95126 15 7 0.0900792 0.220221 7 13 0.0729079 0.864464 13 7 0.0900792 0.220221 7 16 0.0216988 0.972958 16 12 0.0947803 0.791556 12 5 0.0378333 0.067086 5 15 0.0347181 0.95126 15 poisson_cdf_test Normal end of execution. poisson_sample_test Python version: 3.6.9 poisson_mean computes the Poisson mean poisson_sample samples the Poisson distribution poisson_variance computes the Poisson variance. PDF parameter A = 10 PDF mean = 10 PDF variance = 10 Sample size = 1000 Sample mean = 10.084 Sample variance = 10.0229 Sample maximum = 21 Sample minimum = 2 poisson_sample_test Normal end of execution. power_cdf_test Python version: 3.6.9 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 2.24473 0.49883 0.55987 2.24473 1.90713 0.423806 0.404125 1.90713 2.77906 0.617568 0.858129 2.77906 1.56663 0.34814 0.272704 1.56663 2.66853 0.593006 0.791227 2.66853 2.6847 0.596601 0.800848 2.6847 2.74477 0.609949 0.837084 2.74477 2.62972 0.584383 0.768384 2.62972 2.13985 0.475522 0.508773 2.13985 2.14837 0.477416 0.512834 2.14837 power_cdf_test Normal end of execution. power_sample_test Python version: 3.6.9 power_mean computes the Power mean power_sample samples the Power distribution power_variance computes the Power variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 0.5 Sample size = 1000 Sample mean = 2.02016 Sample variance = 0.487097 Sample maximum = 2.99876 Sample minimum = 0.101401 power_sample_test Normal end of execution. psi_values_test: Python version: 3.6.9 psi_values stores values of the PSI function. X PSI(X) 0.100000 -10.4237549404110794 0.200000 -5.2890398965921879 0.300000 -3.5025242222001332 0.400000 -2.5613845445851160 0.500000 -1.9635100260214231 0.600000 -1.5406192138931900 0.700000 -1.2200235536979349 0.800000 -0.9650085667061385 0.900000 -0.7549269499470515 1.000000 -0.5772156649015329 1.100000 -0.4237549404110768 1.200000 -0.2890398965921883 1.300000 -0.1691908888667997 1.400000 -0.0613845445851161 1.500000 0.0364899739785765 1.600000 0.1260474527734763 1.700000 0.2085478748734940 1.800000 0.2849914332938615 1.900000 0.3561841611640597 2.000000 0.4227843350984671 psi_values_test: Normal end of execution. quasigeometric_cdf_test Python version: 3.6.9 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 2 0.125248 0.820285 3 0 0.4825 0.4825 1 6 0.0151049 0.978327 7 2 0.125248 0.820285 3 11 0.00107349 0.99846 11 1 0.212537 0.695037 2 0 0.4825 0.4825 1 1 0.212537 0.695037 2 0 0.4825 0.4825 1 0 0.4825 0.4825 1 quasigeometric_cdf_test Normal end of execution. quasigeometric_sample_test quasigeometric_mean computes the Quasigeometric mean quasigeometric_sample samples the Quasigeometric distribution quasigeometric_variance computes the Quasigeometric variance. PDF parameter A = 0.4825 PDF parameter B = 0.5893 PDF parameter A = 0.4825 PDF mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.307 Sample variance = 3.52675 Sample maximum = 13 Sample minimum = 0 quasigeometric_sample_test Normal end of execution. r8_beta_test: Python version: 3.6.9 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_beta_test: Normal end of execution. r8_csc_test Python version: 3.6.9 r8_csc computes the cosecant of an angle. ANGLE r8_csc(ANGLE) 0.00 Undefined 15.00 1.46037 30.00 -1.00194 45.00 1.29876 60.00 -8.05172 75.00 -1.69796 90.00 1.0177 105.00 -1.18588 120.00 4.05727 135.00 2.06607 150.00 -1.05049 165.00 1.10683 180.00 Undefined 195.00 -2.69119 210.00 1.10311 225.00 -1.05294 240.00 2.09321 255.00 3.94632 270.00 -1.18053 285.00 1.0191 300.00 -1.71484 315.00 -7.61642 330.00 1.29113 345.00 -1.00241 360.00 Undefined r8_csc_test Normal end of execution. r8_erf_test: Python version: 3.6.9 r8_erf evaluates the error function. X ERF(X) r8_erf(X) 0 0 0 0.1 0.1124629160182849 0.1124629160182849 0.2 0.2227025892104785 0.2227025892104785 0.3 0.3286267594591274 0.3286267594591273 0.4 0.4283923550466685 0.4283923550466684 0.5 0.5204998778130465 0.5204998778130465 0.6 0.6038560908479259 0.6038560908479259 0.7 0.6778011938374185 0.6778011938374184 0.8 0.7421009647076605 0.7421009647076605 0.9 0.7969082124228321 0.7969082124228322 1 0.8427007929497149 0.8427007929497148 1.1 0.8802050695740817 0.8802050695740817 1.2 0.9103139782296354 0.9103139782296354 1.3 0.9340079449406524 0.9340079449406524 1.4 0.9522851197626488 0.9522851197626487 1.5 0.9661051464753106 0.9661051464753108 1.6 0.976348383344644 0.976348383344644 1.7 0.9837904585907746 0.9837904585907746 1.8 0.9890905016357306 0.9890905016357308 1.9 0.9927904292352575 0.9927904292352574 2 0.9953222650189527 0.9953222650189527 r8_erf_test Normal end of execution. r8_gamma_inc_test: Python version: 3.6.9 r8_gamma_inc evaluates the normalized incomplete Gamma function P(A,X). A X Exact F r8_gamma_inc(A,X) 0.1 0.03 2.4903 0.738235 0.1 0.3 0.871837 0.908358 0.1 1.5 0.107921 0.988656 0.5 0.075 1.23812 0.301465 0.5 0.75 0.39113 0.779329 0.5 3.5 0.0144472 0.991849 1 0.1 0.904837 0.0951626 1 1 0.367879 0.632121 1 5 0.00673795 0.993262 1.1 0.1 0.882797 0.0720597 1.1 1 0.390833 0.589181 1.1 5 0.00805146 0.991537 2 0.15 0.989814 0.0101858 2 1.5 0.557825 0.442175 2 7 0.00729506 0.992705 6 2.5 114.957 0.042021 6 12 2.44092 0.979659 11 16 280855 0.922604 26 25 8.57648e+24 0.447079 41 45 2.08503e+47 0.744455 r8_gamma_inc_test Normal end of execution. r8_zeta_test Python version: 3.6.9 r8_zeta estimates the Zeta function. P r8_zeta(P) 1 1.79769e+308 2 1.64493 3 1.20206 4 1.08232 5 1.03693 6 1.01734 7 1.00835 8 1.00408 9 1.00201 10 1.00099 11 1.00049 12 1.00025 13 1.00012 14 1.00006 15 1.00003 16 1.00002 17 1.00001 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 3 1.20206 3.125 1.17905 3.25 1.15915 3.375 1.14185 3.5 1.12673 3.625 1.11347 3.75 1.10179 3.875 1.09147 4 1.08232 r8_zeta_test Normal end of execution. r8poly_print_test Python version: 3.6.9 r8poly_print prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 r8poly_print_test: Normal end of execution. r8poly_value_horner_test Python version: 3.6.9 r8poly_value_horner evaluates a polynomial at a point using Horners method. The polynomial coefficients: p(x) = 1 * x^4 - 10 * x^3 + 35 * x^2 - 50 * x + 24 I X P(X) 0 0.0000 24 1 0.3333 10.8642 2 0.6667 3.45679 3 1.0000 0 4 1.3333 -0.987654 5 1.6667 -0.691358 6 2.0000 0 7 2.3333 0.493827 8 2.6667 0.493827 9 3.0000 0 10 3.3333 -0.691358 11 3.6667 -0.987654 12 4.0000 0 13 4.3333 3.45679 14 4.6667 10.8642 15 5.0000 24 r8poly_value_horner_test: Normal end of execution. r8row_max_test Python version: 3.6.9 r8row_max computes maximums of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 Row maximums: 0: 4 1: 8 2: 12 r8row_max_test: Normal end of execution. r8row_mean_test Python version: 3.6.9 r8row_mean computes row means of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 The row means: 0: 2.5 1: 6.5 2: 10.5 r8row_mean_test: Normal end of execution. r8row_min_test Python version: 3.6.9 r8row_min computes minimums of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 Row minimums: 0: 1 1: 5 2: 9 r8row_min_test: Normal end of execution. r8row_variance_test Python version: 3.6.9 r8row_variance computes variances of an R8ROW. The matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 5 6 7 8 2 : 9 10 11 12 The row variances: 0: 1.66667 1: 1.66667 2: 1.66667 r8row_variance_test: Normal end of execution. r8vec_dot_product_test: Python version: 3.6.9 r8vec_dot_product computes the dot product of two R8VEC's. V1 and V2: 0: 0.0596956 0.485868 1: 0.701606 0.838835 2: 0.317686 0.861408 3: 0.809901 0.581036 4: 0.174314 0.753956 5: 0.428125 0.978454 6: 0.513866 0.804851 7: 0.291499 0.335972 8: 0.932295 0.657618 9: 0.420556 0.311879 V1 dot V2 = 3.16788 r8vec_dot_product_test: Normal end of execution. r8vec_transpose_print_test Python version: 3.6.9 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 r8vec_transpose_print_test Normal end of execution. r8vec2_print_test Python version: 3.6.9 r8vec2_print() prints a pair of R8VEC's. Print a pair of R8VEC's: 0: 0 0 1: 0.2 0.04 2: 0.4 0.16 3: 0.6 0.36 4: 0.8 0.64 5: 1 1 r8vec2_print_test: Normal end of execution. rayleigh_cdf_test Python version: 3.6.9 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 2.75403 0.266785 0.612517 2.75403 2.92499 0.250963 0.656801 2.92499 0.169866 0.0423136 0.0036003 0.169866 3.51476 0.187587 0.786515 3.51476 1.7611 0.298782 0.321373 1.7611 4.76172 0.0699527 0.941238 4.76172 4.16258 0.119308 0.885352 4.16258 0.877219 0.199193 0.0917078 0.877219 0.526169 0.127068 0.0340147 0.526169 2.77427 0.265012 0.6179 2.77427 rayleigh_cdf_test Normal end of execution. rayleigh_sample_test Python version: 3.6.9 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 = 2.50812 Sample variance = 1.72893 Sample maximum = 6.63519 Sample minimum = 0.0684439 rayleigh_sample_test Normal end of execution. reciprocal_cdf_test Python version: 3.6.9 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 1.96179 0.463984 0.613371 1.96179 1.48347 0.613587 0.358985 1.48347 1.32559 0.686666 0.256559 1.32559 1.97754 0.460289 0.62065 1.97754 1.23325 0.738079 0.190838 1.23325 2.50943 0.362728 0.83747 2.50943 2.17208 0.419064 0.706058 2.17208 2.20901 0.412057 0.721405 2.20901 2.51587 0.361799 0.839805 2.51587 1.83377 0.496375 0.551946 1.83377 reciprocal_cdf_test Normal end of execution. reciprocal_sample_test Python version: 3.6.9 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 = 1.82628 Sample variance = 0.332797 Sample maximum = 2.99699 Sample minimum = 1.00027 reciprocal_sample_test Normal end of execution. sech_cdf_test Python version: 3.6.9 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 1.82238 0.135059 0.322553 1.82238 4.57922 0.11982 0.728677 4.57922 3.50348 0.154242 0.579298 3.50348 4.33764 0.129171 0.698593 4.33764 0.709551 0.0919625 0.196096 0.709551 1.78719 0.133792 0.317822 1.78719 7.59998 0.031596 0.936385 7.59998 0.476437 0.0834395 0.17566 0.476437 5.24749 0.0935817 0.799919 5.24749 14.8397 0.000854857 0.99829 14.8397 sech_cdf_test Normal end of execution. sech_sample_test Python version: 3.6.9 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 = 3.08278 Sample variance = 9.09735 Sample maximum = 15.9749 Sample minimum = -11.6382 sech_sample_test Normal end of execution. semicircular_cdf_test Python version: 3.6.9 semicircular_cdf evaluates the Semicircular CDF. semicircular_cdf_inv inverts the Semicircular CDF. semicircular_pdf evaluates the Semicircular PDF. PDF parameter A = 3 PDF parameter B = 2 X PDF CDF CDf_inv 2.61582 0.312382 0.378467 2.61572 4.25383 0.247992 0.871152 4.25391 4.35534 0.234074 0.895636 4.35547 2.10167 0.284394 0.223983 2.10156 3.32794 0.314002 0.603915 3.32812 1.40107 0.191212 0.0522482 1.40137 2.49364 0.307939 0.340558 2.49365 4.38784 0.229199 0.903165 4.3877 1.63121 0.232083 0.101229 1.63086 3.25511 0.31571 0.580983 3.25488 semicircular_cdf_test Normal end of execution. semicircular_sample_test Python version: 3.6.9 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 = 2.94933 Sample variance = 0.975703 Sample maximum = 4.94629 Sample minimum = 1.01816 semicircular_sample_test Normal end of execution. sin_power_int_test Python version: 3.6.9 sin_power_int returns values of the integral of SIN(X)^N from A to B. A B N Exact Computed 10.000000 20.000000 0 1.000000e+01 1.000000e+01 0.000000 1.000000 1 4.596977e-01 4.596977e-01 0.000000 1.000000 2 2.726756e-01 2.726756e-01 0.000000 1.000000 3 1.789406e-01 1.789406e-01 0.000000 1.000000 4 1.240256e-01 1.240256e-01 0.000000 1.000000 5 8.897440e-02 8.897440e-02 0.000000 2.000000 5 9.039312e-01 9.039312e-01 1.000000 2.000000 5 8.149568e-01 8.149568e-01 0.000000 1.000000 10 2.188752e-02 2.188752e-02 0.000000 1.000000 11 1.702344e-02 1.702344e-02 sin_power_int_test Normal end of execution. sin_power_int_values_test: Python version: 3.6.9 sin_power_int_values stores values of the cosine power integral. A B N F 10.000000 20.000000 0 10 0.000000 1.000000 1 0.4596976941318603 0.000000 1.000000 2 0.2726756432935796 0.000000 1.000000 3 0.1789405625488581 0.000000 1.000000 4 0.1240255653152068 0.000000 1.000000 5 0.08897439645157594 0.000000 2.000000 5 0.9039312384814995 1.000000 2.000000 5 0.8149568420299235 0.000000 1.000000 10 0.02188752242172985 0.000000 1.000000 11 0.01702343937406933 sin_power_int_values_test: Normal end of execution. stirling2_test: Python version: 3.6.9 stirling2 returns Stirling numbers of the second kind. stirling2 matrix: Col: 0 1 2 3 4 5 6 7 Row 0: 1 0 0 0 0 0 0 0 1: 1 1 0 0 0 0 0 0 2: 1 3 1 0 0 0 0 0 3: 1 7 6 1 0 0 0 0 4: 1 15 25 10 1 0 0 0 5: 1 31 90 65 15 1 0 0 6: 1 63 301 350 140 21 1 0 7: 1 127 966 1701 1050 266 28 1 stirling2_test: Normal end of execution. student_cdf_test Python version: 3.6.9 student_cdf evaluates the Student CDF. student_pdf evaluates the Student PDF. PDF argument X = 2.447 PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF value = 0.14754 CDF value = 0.816049 student_cdf_test Normal end of execution. student_sample_test Python version: 3.6.9 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 = 0.53814 Sample variance = 8.496 Sample maximum = 17.237 Sample minimum = -75.9131 student_sample_test Normal end of execution. student_noncentral_cdf_test Python version: 3.6.9 student_noncentral_cdf evaluates the Student Noncentral CDF PDF argument X = 0.5 PDF parameter IDF = 10 PDF parameter B = 1 CDF value = 0.30528 student_noncentral_cdf_test Normal end of execution. tfn_test Python version: 3.6.9 tfn evaluates Owen's T function. H A T(H,A) Exact 0.0625 0.25 0.0389119 0.0389119 6.5 0.4375 2.00058e-11 2.00058e-11 7 0.96875 6.39906e-13 6.39906e-13 4.78125 0.0625 1.0633e-07 1.0633e-07 2 0.5 0.00862508 0.00862508 1 0.999997 0.0667418 0.0667418 1 0.5 0.0430647 0.0430647 1 1 0.0667419 0.0667419 1 2 0.0784682 0.0784682 1 3 0.0792995 0.0792995 0.5 0.5 0.0644886 0.0644886 0.5 1 0.106671 0.106671 0.5 2 0.141581 0.141581 0.5 3 0.151084 0.151084 0.25 0.5 0.0713466 0.0713466 0.25 1 0.120129 0.120129 0.25 2 0.166613 0.166613 0.25 3 0.18475 0.18475 0.125 0.5 0.0731727 0.0731727 0.125 1 0.123763 0.123763 0.125 2 0.173744 0.173744 0.125 3 0.195119 0.195119 0.0078125 0.5 0.0737894 0.0737894 0.0078125 1 0.124995 0.124995 0.0078125 2 0.176198 0.176198 0.0078125 3 0.198777 0.198777 0.0078125 10 0.234074 0.234089 0.0078125 100 0.233737 0.247946 tfn_test Normal end of execution. triangle_cdf_test Python version: 3.6.9 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 5.57247 0.140557 0.68884 5.57247 3.53565 0.205218 0.3367 3.53565 5.47753 0.14357 0.675353 5.47753 4.77037 0.16602 0.565888 4.77037 7.12689 0.0912097 0.868972 7.12689 4.17815 0.184821 0.462001 4.17815 1.81473 0.090526 0.0368773 1.81473 1.69993 0.0777702 0.0272169 1.69993 7.42261 0.0818219 0.894556 7.42261 7.05181 0.0935932 0.862035 7.05181 triangle_cdf_test Normal end of execution. triangle_sample_test Python version: 3.6.9 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 = 4.64587 Sample variance = 3.60951 Sample maximum = 9.70521 Sample minimum = 1.15826 triangle_sample_test Normal end of execution. triangular_cdf_test Python version: 3.6.9 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 4.20494 0.158269 0.253621 4.20494 4.39259 0.167535 0.28419 4.39259 7.14226 0.141123 0.798354 7.14226 3.47574 0.122259 0.15134 3.47574 3.54784 0.125819 0.160283 3.54784 5.30831 0.212756 0.45831 5.30831 8.35567 0.0812013 0.933239 8.35567 5.04592 0.199799 0.404185 5.04592 7.61246 0.117903 0.85925 7.61246 4.52904 0.174273 0.307509 4.52904 triangular_cdf_test Normal end of execution. triangular_sample_test Python version: 3.6.9 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 = 5.40519 Sample variance = 3.23912 Sample maximum = 9.73286 Sample minimum = 1.06855 triangular_sample_test Normal end of execution. trigamma_test: Python version: 3.6.9 trigamma evaluates the trigamma function. X FX FX Tabulated Computed 1 1.644934066848226 1.644934065473016 1.1 1.433299150792759 1.43329914968199 1.2 1.267377205423779 1.267377204522996 1.3 1.134253434996619 1.134253434263296 1.4 1.025356590529597 1.025356589930374 1.5 0.9348022005446793 0.9348022000532704 1.6 0.8584318931245799 0.8584318927201864 1.7 0.7932328301639984 0.793232829830095 1.8 0.7369741375017002 0.7369741372251055 1.9 0.6879720582426356 0.6879720580127948 2 0.6449340668482264 0.6449340654730159 trigamma_test Normal end of execution. trigamma_values_test: Python version: 3.6.9 trigamma_values stores values of the trigamma function. X trigamma(X) 1.000000 1.6449340668482260 1.100000 1.4332991507927590 1.200000 1.2673772054237791 1.300000 1.1342534349966189 1.400000 1.0253565905295969 1.500000 0.9348022005446793 1.600000 0.8584318931245799 1.700000 0.7932328301639984 1.800000 0.7369741375017002 1.900000 0.6879720582426356 2.000000 0.6449340668482264 trigamma_values_test: Normal end of execution. uniform_01_cdf_test Python version: 3.6.9 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 0.980558 1 0.980558 0.980558 0.724138 1 0.724138 0.724138 0.0190284 1 0.0190284 0.0190284 0.144339 1 0.144339 0.144339 0.415833 1 0.415833 0.415833 0.179284 1 0.179284 0.179284 0.718309 1 0.718309 0.718309 0.732592 1 0.732592 0.732592 0.976242 1 0.976242 0.976242 0.517377 1 0.517377 0.517377 uniform_01_cdf_test Normal end of execution. uniform_01_sample_test Python version: 3.6.9 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 = 0.487928 Sample variance = 0.0821952 Sample maximum = 0.999274 Sample minimum = 0.000221806 uniform_01_sample_test Normal end of execution. uniform_01_order_sample_test Python version: 3.6.9 uniform_order_sample samples the Uniform 01 Order distribution. Ordered sample: 0: 0.0499313 1: 0.120632 2: 0.278323 3: 0.345461 4: 0.421443 5: 0.453921 6: 0.645472 7: 0.683685 8: 0.769824 9: 0.901097 uniform_01_order_sample_test Normal end of execution. uniform_cdf_test Python version: 3.6.9 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 4.29897 0.111111 0.366552 4.29897 1.13183 0.111111 0.0146483 1.13183 7.60643 0.111111 0.734048 7.60643 8.47157 0.111111 0.830174 8.47157 2.73519 0.111111 0.192799 2.73519 2.82553 0.111111 0.202837 2.82553 7.42767 0.111111 0.714186 7.42767 7.45324 0.111111 0.717027 7.45324 4.47884 0.111111 0.386538 4.47884 9.51663 0.111111 0.946292 9.51663 uniform_cdf_test Normal end of execution. uniform_sample_test Python version: 3.6.9 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 = 5.44568 Sample variance = 7.07127 Sample maximum = 9.98553 Sample minimum = 1.00176 uniform_sample_test Normal end of execution. uniform_discrete_cdf_test Python version: 3.6.9 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 5 0.166667 0.833333 6 5 0.166667 0.833333 6 3 0.166667 0.5 4 2 0.166667 0.333333 3 4 0.166667 0.666667 5 3 0.166667 0.5 4 3 0.166667 0.5 4 5 0.166667 0.833333 6 5 0.166667 0.833333 6 4 0.166667 0.666667 5 uniform_discrete_cdf_test Normal end of execution. uniform_discrete_sample_test Python version: 3.6.9 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 = 3.596 Sample variance = 2.91878 Sample maximum = 6 Sample minimum = 1 uniform_discrete_sample_test Normal end of execution. uniform_nsphere_sample_test Python version: 3.6.9 uniform_nsphere_sample samples the Uniform Nsphere distribution. Dimension N of sphere = 3 Points on the sphere: -0.605433 -0.642189 -0.470153 -0.709769 -0.121315 0.693909 -0.230619 0.542392 -0.807852 0.698536 0.506894 0.50508 -0.545142 -0.398564 0.737541 0.27441 0.616327 0.738133 0.59099 0.802597 0.0810502 0.78099 -0.363899 -0.507575 -0.723626 -0.437877 -0.533507 -0.293984 -0.551835 0.780418 uniform_nsphere_sample_test Normal end of execution. von_mises_cdf_test Python version: 3.6.9 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 2.05815 0.186205 0.900968 2.05845 1.12467 0.507939 0.563985 1.12464 0.373594 0.352893 0.213944 0.373369 1.05277 0.514451 0.527197 1.05292 0.846297 0.503864 0.421326 0.846218 0.133949 0.255077 0.14122 0.134068 1.6988 0.322826 0.810516 1.69873 0.889627 0.509645 0.44329 0.889553 1.33562 0.461415 0.666888 1.33556 0.490304 0.400082 0.25791 0.490335 von_mises_cdf_test Normal end of execution. von_mises_sample_test Python version: 3.6.9 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 = 0.962114 Sample circular variance = 0.311479 Sample maximum = 4.10587 Sample minimum = -2.14061 von_mises_sample_test Normal end of execution. weibull_cdf_test Python version: 3.6.9 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 4.19408 0.391812 0.248815 4.19408 5.12091 0.465333 0.690011 5.12091 5.03739 0.483863 0.650342 5.03739 5.05081 0.481225 0.656814 5.05081 4.46085 0.467956 0.364122 4.46085 4.92526 0.500567 0.595056 4.92526 4.50312 0.477016 0.384098 4.50312 5.78435 0.21275 0.920509 5.78435 5.7214 0.23844 0.906312 5.7214 4.92967 0.500095 0.597262 4.92967 weibull_cdf_test Normal end of execution. weibull_sample_test Python version: 3.6.9 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 = 4.66348 Sample variance = 0.569144 Sample maximum = 6.74074 Sample minimum = 2.37805 weibull_sample_test Normal end of execution. weibull_discrete_cdf_test Python version: 3.6.9 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 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 2 0.113508 0.972723 3 1 0.359214 0.859214 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 weibull_discrete_cdf_test Normal end of execution. weibull_discrete_sample_test Python version: 3.6.9 weibull_discrete_sample samples the Weibull Discrete distribution PDF parameter A = 0.5 PDF parameter B = 1.5 Sample size = 1000 Sample mean = 1.17 Sample variance = 0.2071 Sample maximum = 4 Sample minimum = 1 weibull_discrete_sample_test Normal end of execution. zipf_cdf_test Python version: 3.6.9 zipf_pdf evaluates the Zipf PDF. zipf_cdf evaluates the Zipf CDF. zipf_cdf_inv inverts the Zipf CDF. PDF parameter A = 2 X PDF(X) CDF(X) CDf_inv(CDF) 1 0.607927 0.607927 1 2 0.151982 0.759909 2 3 0.0675475 0.827456 3 4 0.0379954 0.865452 4 5 0.0243171 0.889769 5 6 0.0168869 0.906656 6 7 0.0124067 0.919062 7 8 0.00949886 0.928561 8 9 0.00750527 0.936067 9 10 0.00607927 0.942146 10 11 0.00502419 0.94717 11 12 0.00422172 0.951392 12 13 0.0035972 0.954989 13 14 0.00310167 0.958091 14 15 0.0027019 0.960792 15 16 0.00237472 0.963167 16 17 0.00210355 0.965271 17 18 0.00187632 0.967147 18 19 0.00168401 0.968831 19 20 0.00151982 0.970351 20 zipf_cdf_test Normal end of execution. zipf_sample_test Python version: 3.6.9 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 = 1.119 Sample variance = 0.200839 Sample maximum = 7 Sample minimum = 1 zipf_sample_test Normal end of execution. prob_test: Normal end of execution. Tue Oct 19 17:05:41 2021