11-Nov-2022 18:44:08 prob_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test prob(). ANGLE_CDF_TEST(): ANGLE_CDF() evaluates the Angle CDF; PDF parameter N = 5 PDF argument X = 0.500000 CDF value = 0.010781 ANGLE_MEAN_TEST(): ANGLE_MEAN() computes the Angle mean; PDF parameter N = 5 PDF mean = 1.570796 ANGLE_PDF_TEST(): ANGLE_PDF() evaluates the Angle PDF; PDF parameter N = 5 PDF argument X = 0.500000 PDF value = 0.082647 ANGLIT_CDF_TEST(): ANGLIT_CDF() evaluates the Anglit CDF; ANGLIT_CDF_INV() inverts the Anglit CDF. ANGLIT_PDF() evaluates the Anglit PDF; X PDF CDF CDF_INV 0.340421 0.994539 0.814724 0.340421 0.473429 0.986994 0.905792 0.473429 -0.421037 -0.056646 0.126987 -0.421037 0.486654 0.982397 0.913376 0.486654 0.133956 0.869066 0.632359 0.133956 -0.467770 -0.149578 0.097540 -0.467770 -0.229473 0.320684 0.278498 -0.229473 0.046950 0.770292 0.546882 0.046950 0.577771 0.932275 0.957507 0.577771 0.596903 0.917754 0.964889 0.596903 ANGLIT_SAMPLE_TEST(): ANGLIT_MEAN() computes the Anglit mean; ANGLIT_SAMPLE() samples the Anglit distribution; ANGLIT_VARIANCE() computes the Anglit variance. PDF mean = 0 PDF variance = 0.11685 Sample size = 1000 Sample mean = -0.014903 Sample variance = 0.109379 Sample maximum = 0.762849 Sample minimum = -0.762541 ARCSIN_CDF_TEST(): ARCSIN_CDF() evaluates the Arcsin CDF; ARCSIN_CDF_INV() inverts the Arcsin CDF. ARCSIN_PDF() evaluates the Arcsin PDF; PDF parameter A = 1 X PDF CDF CDF_INV -0.837356 0.582283 0.184100 -0.837356 0.651298 0.419479 0.725775 0.651298 -0.396102 0.346665 0.370363 -0.396102 0.878657 0.666683 0.841560 0.878657 0.671221 0.429419 0.734230 0.671221 0.221287 0.326402 0.571026 0.221287 -0.849581 0.603478 0.176855 -0.849581 0.991051 2.384657 0.957384 0.991051 -0.672264 0.429967 0.265322 -0.672264 0.972062 1.356095 0.924581 0.972062 ARCSIN_SAMPLE_TEST(): ARCSIN_MEAN() computes the Arcsin mean; ARCSIN_SAMPLE() samples the Arcsin distribution; ARCSIN_VARIANCE() computes the Arcsin variance. PDF parameter A = 1 PDF mean = 0.000000 PDF variance = 0.500000 Sample size = 1000 Sample mean = 0.019271 Sample variance = 0.489726 Sample maximum = 0.999999 Sample minimum = -0.999999 PDF parameter A = 16 PDF mean = 0.000000 PDF variance = 128.000000 Sample size = 1000 Sample mean = 0.534066 Sample variance = 127.873553 Sample maximum = 15.999997 Sample minimum = -15.999966 benford_cdf_test(): benford_cdf() evaluates the Benford CDF. benford_cdf_inv() inverts the Benford CDF. benford_pdf() evaluates the Benford PDF. N CDF(N) CDF(N) by summing 1 0.30103 0.30103 2 0.477121 0.477121 3 0.60206 0.60206 4 0.69897 0.69897 5 0.778151 0.778151 6 0.845098 0.845098 7 0.90309 0.90309 8 0.954243 0.954243 9 1 1 N CDF(N) CDF(N) by summing 10 0.0413927 0.0413927 11 0.0791812 0.0791812 12 0.113943 0.113943 13 0.146128 0.146128 14 0.176091 0.176091 15 0.20412 0.20412 16 0.230449 0.230449 17 0.255273 0.255273 18 0.278754 0.278754 19 0.30103 0.30103 20 0.322219 0.322219 21 0.342423 0.342423 22 0.361728 0.361728 23 0.380211 0.380211 24 0.39794 0.39794 25 0.414973 0.414973 26 0.431364 0.431364 27 0.447158 0.447158 28 0.462398 0.462398 29 0.477121 0.477121 30 0.491362 0.491362 31 0.50515 0.50515 32 0.518514 0.518514 33 0.531479 0.531479 34 0.544068 0.544068 35 0.556303 0.556303 36 0.568202 0.568202 37 0.579784 0.579784 38 0.591065 0.591065 39 0.60206 0.60206 40 0.612784 0.612784 41 0.623249 0.623249 42 0.633468 0.633468 43 0.643453 0.643453 44 0.653213 0.653213 45 0.662758 0.662758 46 0.672098 0.672098 47 0.681241 0.681241 48 0.690196 0.690196 49 0.69897 0.69897 50 0.70757 0.70757 51 0.716003 0.716003 52 0.724276 0.724276 53 0.732394 0.732394 54 0.740363 0.740363 55 0.748188 0.748188 56 0.755875 0.755875 57 0.763428 0.763428 58 0.770852 0.770852 59 0.778151 0.778151 60 0.78533 0.78533 61 0.792392 0.792392 62 0.799341 0.799341 63 0.80618 0.80618 64 0.812913 0.812913 65 0.819544 0.819544 66 0.826075 0.826075 67 0.832509 0.832509 68 0.838849 0.838849 69 0.845098 0.845098 70 0.851258 0.851258 71 0.857332 0.857332 72 0.863323 0.863323 73 0.869232 0.869232 74 0.875061 0.875061 75 0.880814 0.880814 76 0.886491 0.886491 77 0.892095 0.892095 78 0.897627 0.897627 79 0.90309 0.90309 80 0.908485 0.908485 81 0.913814 0.913814 82 0.919078 0.919078 83 0.924279 0.924279 84 0.929419 0.929419 85 0.934498 0.934498 86 0.939519 0.939519 87 0.944483 0.944483 88 0.94939 0.94939 89 0.954243 0.954243 90 0.959041 0.959041 91 0.963788 0.963788 92 0.968483 0.968483 93 0.973128 0.973128 94 0.977724 0.977724 95 0.982271 0.982271 96 0.986772 0.986772 97 0.991226 0.991226 98 0.995635 0.995635 99 1 1 X PDF CDF CDF_INV 7 0.0579919 0.90309 7 1 0.30103 0.30103 2 1 0.30103 0.30103 2 3 0.124939 0.60206 4 2 0.176091 0.477121 3 2 0.176091 0.477121 3 4 0.09691 0.69897 5 8 0.0511525 0.954243 9 4 0.09691 0.69897 5 1 0.30103 0.30103 2 BENFORD_PDF_TEST(): BENFORD_PDF() evaluates the Benford PDF. N PDF(N) 1 0.30103 2 0.176091 3 0.124939 4 0.09691 5 0.0791812 6 0.0669468 7 0.0579919 8 0.0511525 9 0.0457575 N PDF(N) 10 0.0413927 11 0.0377886 12 0.0347621 13 0.0321847 14 0.0299632 15 0.0280287 16 0.0263289 17 0.0248236 18 0.0234811 19 0.0222764 20 0.0211893 21 0.0202034 22 0.0193052 23 0.0184834 24 0.0177288 25 0.0170333 26 0.0163904 27 0.0157943 28 0.01524 29 0.0147233 30 0.0142404 31 0.0137883 32 0.013364 33 0.012965 34 0.0125891 35 0.0122345 36 0.0118992 37 0.0115819 38 0.011281 39 0.0109954 40 0.0107239 41 0.0104654 42 0.0102192 43 0.00998422 44 0.00975984 45 0.00954532 46 0.00934003 47 0.00914338 48 0.00895484 49 0.00877392 50 0.00860017 51 0.00843317 52 0.00827253 53 0.00811789 54 0.00796893 55 0.00782534 56 0.00768683 57 0.00755314 58 0.00742402 59 0.00729924 60 0.00717858 61 0.00706185 62 0.00694886 63 0.00683942 64 0.00673338 65 0.00663058 66 0.00653087 67 0.00643411 68 0.00634018 69 0.00624895 70 0.00616031 71 0.00607415 72 0.00599036 73 0.00590886 74 0.00582954 75 0.00575233 76 0.00567713 77 0.00560388 78 0.00553249 79 0.0054629 80 0.00539503 81 0.00532883 82 0.00526424 83 0.00520119 84 0.00513964 85 0.00507953 86 0.0050208 87 0.00496342 88 0.00490733 89 0.0048525 90 0.00479888 91 0.00474644 92 0.00469512 93 0.00464491 94 0.00459575 95 0.00454763 96 0.0045005 97 0.00445434 98 0.00440912 99 0.00436481 benford_sample_test(): benford_mean() computes the Benford mean; benford_sample() samples the Benford distribution; benford_variance() computes the benford variance. PDF mean = 3.440237 PDF variance = 6.056513 Sample size = 10000 Sample mean = 3.424500 Sample variance = 5.999300 Sample maximum = 9 Sample minimum = 1 BERNOULLI_CDF_TEST() BERNOULLI_CDF() evaluates the Bernoulli CDF; BERNOULLI_CDF_INV() inverts the Bernoulli CDF. BERNOULLI_PDF() evaluates the Bernoulli PDF; PDF parameter A = 0.750000 X PDF CDF CDF_INV 1 0.750000 1.000000 1 0 0.250000 0.250000 0 1 0.750000 1.000000 1 0 0.250000 0.250000 0 1 0.750000 1.000000 1 1 0.750000 1.000000 1 1 0.750000 1.000000 1 0 0.250000 0.250000 0 1 0.750000 1.000000 1 0 0.250000 0.250000 0 BERNOULLI_SAMPLE_TEST(): BERNOULLI_MEAN() computes the Bernoulli mean; BERNOULLI_SAMPLE() samples the Bernoulli distribution; BERNOULLI_VARIANCE() computes the Bernoulli variance. PDF parameter A = 0.750000 PDF mean = 0.750000 PDF variance = 0.187500 Sample size = 1000 Sample mean = 0.762000 Sample variance = 0.181538 Sample maximum = 1 Sample minimum = 0 BESSEL_I0_TEST(): BESSEL_I0() evaluates the Bessel function I0(X); X Exact F I0(X) 0.000000 1.000000 1.000000 0.200000 1.010025 1.010025 0.400000 1.040402 1.040402 0.600000 1.092045 1.092045 0.800000 1.166515 1.166515 1.000000 1.266066 1.266066 1.200000 1.393726 1.393726 1.400000 1.553395 1.553395 1.600000 1.749981 1.749981 1.800000 1.989559 1.989559 2.000000 2.279585 2.279585 2.500000 3.289839 3.289839 3.000000 4.880793 4.880793 3.500000 7.378203 7.378203 4.000000 11.301922 11.301922 4.500000 17.481172 17.481172 5.000000 27.239872 27.239872 6.000000 67.234407 67.234407 8.000000 427.564116 427.564116 10.000000 2815.716628 2815.716628 BESSEL_I1_TEST(): BESSEL_I1() evaluates the Bessel function I1(X); X Exact F I1(X) 0.000000 0 0 0.200000 0.100501 0.100501 0.400000 0.204027 0.204027 0.600000 0.313704 0.313704 0.800000 0.432865 0.432865 1.000000 0.565159 0.565159 1.200000 0.714678 0.714678 1.400000 0.886092 0.886092 1.600000 1.08481 1.08481 1.800000 1.31717 1.31717 2.000000 1.59064 1.59064 2.500000 2.51672 2.51672 3.000000 3.95337 3.95337 3.500000 6.20583 6.20583 4.000000 9.75947 9.75947 4.500000 15.3892 15.3892 5.000000 24.3356 24.3356 6.000000 61.3419 61.3419 8.000000 399.873 399.873 10.000000 2670.99 2670.99 BETA_BINOMIAL_CDF_TEST(): BETA_BINOMIAL_CDF() evaluates the Beta Binomial CDF; BETA_BINOMIAL_CDF_INV() inverts the Beta Binomial CDF. BETA_BINOMIAL_PDF() evaluates the Beta Binomial PDF; PDF parameter A = 2.000000 PDF parameter B = 3.000000 PDF parameter C = 4 X PDF CDF CDF_INV 1 0.285714 0.500000 1 1 0.285714 0.500000 1 1 0.285714 0.500000 1 1 0.285714 0.500000 1 0 0.214286 0.214286 0 2 0.257143 0.757143 2 1 0.285714 0.500000 1 1 0.285714 0.500000 1 2 0.257143 0.757143 2 0 0.214286 0.214286 0 BETA_BINOMIAL_SAMPLE_TEST() BETA_BINOMIAL_MEAN() computes the Beta Binomial mean; BETA_BINOMIAL_SAMPLE() samples the Beta Binomial distribution; BETA_BINOMIAL_VARIANCE() computes the Beta Binomial variance. PDF parameter A = 2.000000 PDF parameter B = 3.000000 PDF parameter C = 4 PDF mean = 1.600000 PDF variance = 1.440000 Sample size = 1000 Sample mean = 1.558000 Sample variance = 1.452088 Sample maximum = 4 Sample minimum = 0 BETA_CDF_TEST(): BETA_CDF() evaluates the Beta CDF; BETA_CDF_INV() inverts the Beta CDF. BETA_PDF() evaluates the Beta PDF; PDF parameter A = 12 PDF parameter B = 12 A B X PDF CDF CDF_INV 12.000000 12.000000 0.624426 1.914811 0.889880 0.624426 12.000000 12.000000 0.593122 2.623453 0.818843 0.593122 12.000000 12.000000 0.309342 0.686923 0.027300 0.309342 12.000000 12.000000 0.414907 2.799728 0.202933 0.414907 12.000000 12.000000 0.669857 1.003948 0.955240 0.669857 12.000000 12.000000 0.487715 3.842715 0.452582 0.487715 12.000000 12.000000 0.463469 3.647154 0.361410 0.463469 12.000000 12.000000 0.262932 0.234990 0.007201 0.262932 12.000000 12.000000 0.516304 3.823321 0.562825 0.516304 12.000000 12.000000 0.574000 3.031924 0.764709 0.574000 BETA_INC_TEST(): BETA_INC() evaluates the normalized incomplete Beta function BETA_INC(A,B,X). A B X Exact F BETA_INC(A,B,X) 0.500000 0.500000 0.010000 0.063769 0.063769 0.500000 0.500000 0.100000 0.204833 0.204833 0.500000 0.500000 1.000000 1.000000 1.000000 1.000000 0.500000 0.000000 0.000000 0.000000 1.000000 0.500000 0.010000 0.005013 0.005013 1.000000 0.500000 0.100000 0.051317 0.051317 1.000000 0.500000 0.500000 0.292893 0.292893 1.000000 1.000000 0.500000 0.500000 0.500000 2.000000 2.000000 0.100000 0.028000 0.028000 2.000000 2.000000 0.200000 0.104000 0.104000 2.000000 2.000000 0.300000 0.216000 0.216000 2.000000 2.000000 0.400000 0.352000 0.352000 2.000000 2.000000 0.500000 0.500000 0.500000 2.000000 2.000000 0.600000 0.648000 0.648000 2.000000 2.000000 0.700000 0.784000 0.784000 2.000000 2.000000 0.800000 0.896000 0.896000 2.000000 2.000000 0.900000 0.972000 0.972000 5.500000 5.000000 0.500000 0.436191 0.436191 10.000000 0.500000 0.900000 0.151641 0.151641 10.000000 5.000000 0.500000 0.089783 0.089783 10.000000 5.000000 1.000000 1.000000 1.000000 10.000000 10.000000 0.500000 0.500000 0.500000 20.000000 5.000000 0.800000 0.459877 0.459877 20.000000 10.000000 0.600000 0.214682 0.214682 20.000000 10.000000 0.800000 0.950736 0.950736 20.000000 20.000000 0.500000 0.500000 0.500000 20.000000 20.000000 0.600000 0.897941 0.897941 30.000000 10.000000 0.700000 0.224130 0.224130 30.000000 10.000000 0.800000 0.758641 0.758641 40.000000 20.000000 0.700000 0.700178 0.700178 1.000000 0.500000 0.100000 0.051317 0.051317 1.000000 0.500000 0.200000 0.105573 0.105573 1.000000 0.500000 0.300000 0.163340 0.163340 1.000000 0.500000 0.400000 0.225403 0.225403 1.000000 2.000000 0.200000 0.360000 0.360000 1.000000 3.000000 0.200000 0.488000 0.488000 1.000000 4.000000 0.200000 0.590400 0.590400 1.000000 5.000000 0.200000 0.672320 0.672320 2.000000 2.000000 0.300000 0.216000 0.216000 3.000000 2.000000 0.300000 0.083700 0.083700 4.000000 2.000000 0.300000 0.030780 0.030780 5.000000 2.000000 0.300000 0.010935 0.010935 1.306250 11.756200 0.225609 0.918885 0.918885 1.306250 11.756200 0.033557 0.210530 0.210530 1.306250 11.756200 0.029522 0.182413 0.182413 BETA_SAMPLE_TEST(): BETA_MEAN() computes the Beta mean; BETA_SAMPLE() samples the Beta distribution; BETA_VARIANCE() computes the Beta variance. PDF parameter A = 2.000000 PDF parameter B = 3.000000 PDF mean = 0.400000 PDF variance = 0.040000 Sample size = 1000 Sample mean = 0.404236 Sample variance = 0.041634 Sample maximum = 0.915445 Sample minimum = 0.002279 BINOMIAL_CDF_TEST(): BINOMIAL_CDF() evaluates the Binomial CDF; BINOMIAL_CDF_INV() inverts the Binomial CDF. BINOMIAL_PDF() evaluates the Binomial PDF; PDF parameter A = 5.000000 PDF parameter B = 0.650000 X PDF CDF CDF_INV 4 0.312386 0.883971 4 4 0.312386 0.883971 4 2 0.181147 0.235169 2 3 0.336416 0.571585 3 5 0.116029 1.000000 5 5 0.116029 1.000000 5 3 0.336416 0.571585 3 5 0.116029 1.000000 5 2 0.181147 0.235169 2 4 0.312386 0.883971 4 BINOMIAL_SAMPLE_TEST(): BINOMIAL_MEAN() computes the Binomial mean; BINOMIAL_SAMPLE() samples the Binomial distribution; BINOMIAL_VARIANCE() computes the Binomial variance. PDF parameter A = 5 PDF parameter B = 0.300000 PDF mean = 1.500000 PDF variance = 1.050000 Sample size = 1000 Sample mean = 1.513000 Sample variance = 1.112944 Sample maximum = 5 Sample minimum = 0 BIRTHDAY_CDF_TEST(): BIRTHDAY_CDF() evaluates the Birthday CDF; BIRTHDAY_CDF_INV() inverts the Birthday CDF. BIRTHDAY_PDF() evaluates the Birthday PDF; N PDF CDF CDF_INV 1 0 0 1 2 0.00273973 0.00273973 2 3 0.00546444 0.00820417 3 4 0.00815175 0.0163559 4 5 0.0107797 0.0271356 5 6 0.0133269 0.0404625 6 7 0.0157732 0.0562357 7 8 0.0180996 0.0743353 8 9 0.0202885 0.0946238 9 10 0.0223243 0.116948 10 11 0.0241932 0.141141 11 12 0.0258834 0.167025 12 13 0.0273855 0.19441 13 14 0.0286922 0.223103 14 15 0.0297988 0.252901 15 16 0.0307027 0.283604 16 17 0.0314037 0.315008 17 18 0.0319038 0.346911 18 19 0.0322071 0.379119 19 20 0.0323199 0.411438 20 21 0.03225 0.443688 21 22 0.032007 0.475695 22 23 0.0316019 0.507297 23 24 0.031047 0.538344 24 25 0.0303554 0.5687 25 26 0.0295411 0.598241 26 27 0.0286185 0.626859 27 28 0.0276022 0.654461 28 29 0.0265071 0.680969 29 30 0.0253477 0.706316 30 BIRTHDAY_SAMPLE_TEST(): BIRTHDAY_SAMPLE() samples the Birthday distribution. N Mean PDF 10 0.0247 0.0223243 11 0.0233 0.0241932 12 0.0264 0.0258834 13 0.0289 0.0273855 14 0.0288 0.0286922 15 0.0291 0.0297988 16 0.0319 0.0307027 17 0.0333 0.0314037 18 0.0328 0.0319038 19 0.032 0.0322071 20 0.0339 0.0323199 21 0.0368 0.03225 22 0.0327 0.032007 23 0.0319 0.0316019 24 0.0315 0.031047 25 0.0322 0.0303554 26 0.028 0.0295411 27 0.0289 0.0286185 28 0.0242 0.0276022 29 0.0252 0.0265071 30 0.0247 0.0253477 31 0.0248 0.0241384 32 0.0231 0.0228929 33 0.0211 0.0216243 34 0.0215 0.020345 35 0.0169 0.0190664 36 0.0166 0.0177989 37 0.0192 0.0165519 38 0.0159 0.0153338 39 0.013 0.0141518 40 0.0126 0.0130121 BRADFORD_CDF_TEST(): BRADFORD_CDF() evaluates the Bradford CDF; BRADFORD_CDF_INV() inverts the Bradford CDF. BRADFORD_PDF() evaluates the Bradford PDF; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 1.410542 0.969716 0.579047 1.410542 1.099732 1.665678 0.188810 1.099732 1.014326 2.074866 0.030355 1.014326 1.894915 0.587298 0.940782 1.894915 1.693611 0.702421 0.811660 1.693611 1.489922 0.876214 0.652187 1.489922 1.344652 1.063957 0.512144 1.344652 1.243343 1.250871 0.395398 1.243343 1.330384 1.086830 0.496802 1.330384 1.420434 0.956990 0.588577 1.420434 BRADFORD_SAMPLE_TEST(): BRADFORD_MEAN() computes the Bradford mean; BRADFORD_SAMPLE() samples the Bradford distribution; BRADFORD_VARIANCE() computes the Bradford variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 1.38801 PDF variance = 0.0807807 Sample size = 1000 Sample mean = 1.37505 Sample variance = 0.0802779 Sample maximum = 1.99998 Sample minimum = 1.00022 BUFFON_BOX_PDF_TEST(): BUFFON_BOX_PDF() evaluates the Buffon-Laplace PDF, the probability that, on a grid of cells of width A and height B, a needle of length L, dropped at random, will cross at least one grid line. A B L PDF 1.0000 1.0000 0.0000 0.000000 1.0000 1.0000 0.2000 0.241916 1.0000 1.0000 0.4000 0.458366 1.0000 1.0000 0.6000 0.649352 1.0000 1.0000 0.8000 0.814873 1.0000 1.0000 1.0000 0.954930 1.0000 2.0000 0.0000 0.000000 1.0000 2.0000 0.2000 0.184620 1.0000 2.0000 0.4000 0.356507 1.0000 2.0000 0.6000 0.515662 1.0000 2.0000 0.8000 0.662085 1.0000 2.0000 1.0000 0.795775 1.0000 3.0000 0.0000 0.000000 1.0000 3.0000 0.2000 0.165521 1.0000 3.0000 0.4000 0.322554 1.0000 3.0000 0.6000 0.471099 1.0000 3.0000 0.8000 0.611155 1.0000 3.0000 1.0000 0.742723 1.0000 4.0000 0.0000 0.000000 1.0000 4.0000 0.2000 0.155972 1.0000 4.0000 0.4000 0.305577 1.0000 4.0000 0.6000 0.448817 1.0000 4.0000 0.8000 0.585690 1.0000 4.0000 1.0000 0.716197 1.0000 5.0000 0.0000 0.000000 1.0000 5.0000 0.2000 0.150242 1.0000 5.0000 0.4000 0.295392 1.0000 5.0000 0.6000 0.435448 1.0000 5.0000 0.8000 0.570411 1.0000 5.0000 1.0000 0.700282 2.0000 1.0000 0.0000 0.000000 2.0000 1.0000 0.2000 0.184620 2.0000 1.0000 0.4000 0.356507 2.0000 1.0000 0.6000 0.515662 2.0000 1.0000 0.8000 0.662085 2.0000 1.0000 1.0000 0.795775 2.0000 2.0000 0.0000 0.000000 2.0000 2.0000 0.4000 0.241916 2.0000 2.0000 0.8000 0.458366 2.0000 2.0000 1.2000 0.649352 2.0000 2.0000 1.6000 0.814873 2.0000 2.0000 2.0000 0.954930 2.0000 3.0000 0.0000 0.000000 2.0000 3.0000 0.4000 0.203718 2.0000 3.0000 0.8000 0.390460 2.0000 3.0000 1.2000 0.560225 2.0000 3.0000 1.6000 0.713014 2.0000 3.0000 2.0000 0.848826 2.0000 4.0000 0.0000 0.000000 2.0000 4.0000 0.4000 0.184620 2.0000 4.0000 0.8000 0.356507 2.0000 4.0000 1.2000 0.515662 2.0000 4.0000 1.6000 0.662085 2.0000 4.0000 2.0000 0.795775 2.0000 5.0000 0.0000 0.000000 2.0000 5.0000 0.4000 0.173161 2.0000 5.0000 0.8000 0.336135 2.0000 5.0000 1.2000 0.488924 2.0000 5.0000 1.6000 0.631527 2.0000 5.0000 2.0000 0.763944 3.0000 1.0000 0.0000 0.000000 3.0000 1.0000 0.2000 0.165521 3.0000 1.0000 0.4000 0.322554 3.0000 1.0000 0.6000 0.471099 3.0000 1.0000 0.8000 0.611155 3.0000 1.0000 1.0000 0.742723 3.0000 2.0000 0.0000 0.000000 3.0000 2.0000 0.4000 0.203718 3.0000 2.0000 0.8000 0.390460 3.0000 2.0000 1.2000 0.560225 3.0000 2.0000 1.6000 0.713014 3.0000 2.0000 2.0000 0.848826 3.0000 3.0000 0.0000 0.000000 3.0000 3.0000 0.6000 0.241916 3.0000 3.0000 1.2000 0.458366 3.0000 3.0000 1.8000 0.649352 3.0000 3.0000 2.4000 0.814873 3.0000 3.0000 3.0000 0.954930 3.0000 4.0000 0.0000 0.000000 3.0000 4.0000 0.6000 0.213268 3.0000 4.0000 1.2000 0.407437 3.0000 4.0000 1.8000 0.582507 3.0000 4.0000 2.4000 0.738479 3.0000 4.0000 3.0000 0.875352 3.0000 5.0000 0.0000 0.000000 3.0000 5.0000 0.6000 0.196079 3.0000 5.0000 1.2000 0.376879 3.0000 5.0000 1.8000 0.542400 3.0000 5.0000 2.4000 0.692642 3.0000 5.0000 3.0000 0.827606 4.0000 1.0000 0.0000 0.000000 4.0000 1.0000 0.2000 0.155972 4.0000 1.0000 0.4000 0.305577 4.0000 1.0000 0.6000 0.448817 4.0000 1.0000 0.8000 0.585690 4.0000 1.0000 1.0000 0.716197 4.0000 2.0000 0.0000 0.000000 4.0000 2.0000 0.4000 0.184620 4.0000 2.0000 0.8000 0.356507 4.0000 2.0000 1.2000 0.515662 4.0000 2.0000 1.6000 0.662085 4.0000 2.0000 2.0000 0.795775 4.0000 3.0000 0.0000 0.000000 4.0000 3.0000 0.6000 0.213268 4.0000 3.0000 1.2000 0.407437 4.0000 3.0000 1.8000 0.582507 4.0000 3.0000 2.4000 0.738479 4.0000 3.0000 3.0000 0.875352 4.0000 4.0000 0.0000 0.000000 4.0000 4.0000 0.8000 0.241916 4.0000 4.0000 1.6000 0.458366 4.0000 4.0000 2.4000 0.649352 4.0000 4.0000 3.2000 0.814873 4.0000 4.0000 4.0000 0.954930 4.0000 5.0000 0.0000 0.000000 4.0000 5.0000 0.8000 0.218997 4.0000 5.0000 1.6000 0.417623 4.0000 5.0000 2.4000 0.595876 4.0000 5.0000 3.2000 0.753758 4.0000 5.0000 4.0000 0.891268 5.0000 1.0000 0.0000 0.000000 5.0000 1.0000 0.2000 0.150242 5.0000 1.0000 0.4000 0.295392 5.0000 1.0000 0.6000 0.435448 5.0000 1.0000 0.8000 0.570411 5.0000 1.0000 1.0000 0.700282 5.0000 2.0000 0.0000 0.000000 5.0000 2.0000 0.4000 0.173161 5.0000 2.0000 0.8000 0.336135 5.0000 2.0000 1.2000 0.488924 5.0000 2.0000 1.6000 0.631527 5.0000 2.0000 2.0000 0.763944 5.0000 3.0000 0.0000 0.000000 5.0000 3.0000 0.6000 0.196079 5.0000 3.0000 1.2000 0.376879 5.0000 3.0000 1.8000 0.542400 5.0000 3.0000 2.4000 0.692642 5.0000 3.0000 3.0000 0.827606 5.0000 4.0000 0.0000 0.000000 5.0000 4.0000 0.8000 0.218997 5.0000 4.0000 1.6000 0.417623 5.0000 4.0000 2.4000 0.595876 5.0000 4.0000 3.2000 0.753758 5.0000 4.0000 4.0000 0.891268 5.0000 5.0000 0.0000 0.000000 5.0000 5.0000 1.0000 0.241916 5.0000 5.0000 2.0000 0.458366 5.0000 5.0000 3.0000 0.649352 5.0000 5.0000 4.0000 0.814873 5.0000 5.0000 5.0000 0.954930 BUFFON_BOX_SAMPLE_TEST(): BUFFON_BOX_SAMPLE() simulates a Buffon-Laplace needle dropping experiment. On a grid of cells of width A and height B a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1.000000 Cell height B = 1.000000 Needle length L = 1.000000 Trials Hits Est(Pi) Err 10 10 3.000000 0.141593 100 98 3.061224 0.080368 10000 9543 3.143666 0.002073 1000000 954799 3.142023 0.000430 BUFFON_PDF_TEST(): BUFFON_PDF() evaluates the Buffon PDF, the probability that, on a grid of cells of width A, a needle of length L, dropped at random, will cross at least one grid line. A L PDF 1.0000 0.0000 0.000000 1.0000 0.2000 0.127324 1.0000 0.4000 0.254648 1.0000 0.6000 0.381972 1.0000 0.8000 0.509296 1.0000 1.0000 0.636620 2.0000 0.0000 0.000000 2.0000 0.4000 0.127324 2.0000 0.8000 0.254648 2.0000 1.2000 0.381972 2.0000 1.6000 0.509296 2.0000 2.0000 0.636620 3.0000 0.0000 0.000000 3.0000 0.6000 0.127324 3.0000 1.2000 0.254648 3.0000 1.8000 0.381972 3.0000 2.4000 0.509296 3.0000 3.0000 0.636620 4.0000 0.0000 0.000000 4.0000 0.8000 0.127324 4.0000 1.6000 0.254648 4.0000 2.4000 0.381972 4.0000 3.2000 0.509296 4.0000 4.0000 0.636620 5.0000 0.0000 0.000000 5.0000 1.0000 0.127324 5.0000 2.0000 0.254648 5.0000 3.0000 0.381972 5.0000 4.0000 0.509296 5.0000 5.0000 0.636620 BUFFON_SAMPLE_TEST(): BUFFON_SAMPLE() simulates a Buffon-Laplace needle dropping experiment. On a grid of cells of width A, a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1.000000 Needle length L = 1.000000 Trials Hits Est(Pi) Err 10 9 2.222222 0.919370 100 64 3.125000 0.016593 10000 6353 3.148119 0.006526 1000000 637214 3.138663 0.002930 BURR_CDF_TEST(): BURR_CDF() evaluates the Burr CDF; BURR_CDF_INV() inverts the Burr CDF. BURR_PDF() evaluates the Burr PDF; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF parameter D = 2 X PDF CDF CDF_INV 3.85382 0.102554 0.934432 3.85382 3.29331 0.250144 0.840974 3.29331 1.54535 0.210018 0.0393464 1.54535 1.29181 0.0632738 0.00618336 1.29181 2.59716 0.556482 0.561002 2.59716 3.31057 0.243785 0.845235 3.31057 2.4131 0.60504 0.453507 2.4131 2.52055 0.581395 0.517378 2.52055 2.07013 0.56006 0.248026 2.07013 4.72992 0.0248674 0.982158 4.72992 BURR_SAMPLE_TEST(): BURR_MEAN() computes the Burr mean; BURR_VARIANCE() computes the Burr variance; BURR_SAMPLE() samples the Burr distribution; PDF parameter A = 2 PDF parameter B = 2 PDF parameter C = 3 PDF parameter D = 2 PDF mean = 3.61227 PDF variance = 0.62513 Sample size = 1000 Sample mean = 3.65726 Sample variance = 0.646348 Sample maximum = 10.7233 Sample minimum = 2.13306 cardioid_cdf_test(): cardioid_cdf evaluates the Cardioid CDF; cardioid_cdf_inv inverts the Cardioid CDF. cardioid_pdf evaluates the Cardioid PDF; PDF parameter A = 0 PDF parameter B = 0.25 X PDF CDF CDF_INV 1.514974 0.163595 0.820569 1.514974 -0.106851 0.238279 0.474507 -0.106851 -3.036477 0.080017 0.008380 -3.036476 -1.489608 0.165609 0.183606 -1.489608 -0.381905 0.232999 0.409560 -0.381904 2.149087 0.115658 0.908676 2.149087 -0.330526 0.234425 0.421569 -0.330526 -2.537193 0.093675 0.050972 -2.537190 1.861616 0.136337 0.872521 1.861616 1.158458 0.191046 0.757282 1.158458 cardioid_sample_test(): cardioid_mean() computes the Cardioid mean; cardioid_sample() samples the Cardioid distribution; cardioid_variance() computes the Cardioid variance. PDF parameter A = 0 PDF parameter B = 0.25 PDF mean = 0.000000 PDF variance = 0.000000 Sample size = 1000 Sample mean = -0.058928 Sample variance = 2.318550 Sample maximum = 3.139182 Sample minimum = -3.139942 cauchy_cdf_test(): cauchy_cdf() evaluates the Cauchy CDF; cauchy_cdf_inv() inverts the Cauchy CDF. cauchy_pdf() evaluates the Cauchy PDF; PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV -0.781044 0.057065 0.262050 -0.781044 0.444487 0.083622 0.347739 0.444487 2.887272 0.097569 0.591533 2.887272 1.725294 0.105221 0.470934 1.725294 8.829043 0.017164 0.868245 8.829043 7.802341 0.022381 0.848109 7.802341 -2.747375 0.030279 0.179389 -2.747375 1.969222 0.106092 0.496734 1.969222 -2.884349 0.029063 0.175325 -2.884349 -0.352798 0.065696 0.288301 -0.352798 CAUCHY_SAMPLE_TEST(): 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 = Inf Sample size = 1000 Sample mean = 0.208973 Sample variance = 15743.4 Sample maximum = 2371.39 Sample minimum = -2487.93 CHEBYSHEV1_CDF_TEST(): CHEBYSHEV1_CDF() evaluates the Chebyshev1 CDF; CHEBYSHEV1_CDF_INV() inverts the Chebyshev1 CDF. CHEBYSHEV1_PDF() evaluates the Chebyshev1 PDF; X PDF CDF CDF_INV -0.409277 0.348867 0.365781 -0.409277 -0.91159 0.774286 0.134856 -0.91159 -0.997222 4.27374 0.0237298 -0.997222 0.939813 0.931575 0.889001 0.939813 0.480155 0.362877 0.659419 0.480155 -0.465411 0.359634 0.345906 -0.465411 0.246035 0.328405 0.579128 0.246035 -0.792169 0.521561 0.208952 -0.792169 -0.789487 0.518616 0.210347 -0.789487 0.74079 0.473861 0.765549 0.74079 CHEBYSHEV1_SAMPLE_TEST(): CHEBYSHEV1_MEAN() computes the Chebyshev1 mean; CHEBYSHEV1_SAMPLE() samples the Chebyshev1 distribution; CHEBYSHEV1_VARIANCE() computes the Chebyshev1 variance. PDF mean = 0 PDF variance = 0.5 Sample size = 1000 Sample mean = 0.00821605 Sample variance = 0.499786 Sample maximum = 1 Sample minimum = -0.99999 CHI_CDF_TEST(): CHI_CDF() evaluates the Chi CDF. CHI_CDF_INV() inverts the Chi CDF. CHI_PDF() evaluates the Chi PDF. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 3.774977 0.293314 0.411908 3.774902 5.296290 0.183234 0.797701 5.295898 4.510742 0.263358 0.620745 4.510742 4.974343 0.218725 0.732959 4.974609 3.376615 0.278061 0.297293 3.376953 6.988475 0.040426 0.970246 6.988281 4.529224 0.261844 0.625598 4.529297 2.757318 0.209365 0.143858 2.757324 4.275802 0.279860 0.556828 4.275879 3.414802 0.280577 0.307960 3.415039 CHI_SAMPLE_TEST(): CHI_MEAN() computes the Chi mean; CHI_VARIANCE() computes the Chi variance; CHI_SAMPLE() samples the Chi distribution. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 4.19154 PDF variance = 1.81408 Sample size = 1000 Sample mean = 4.23943 Sample variance = 1.88577 Sample maximum = 9.74307 Sample minimum = 1.36111 CHI_SQUARE_CDF_TEST(): CHI_SQUARE_CDF() evaluates the Chi Square CDF; CHI_SQUARE_CDF_INV() inverts the Chi Square CDF. CHI_SQUARE_PDF() evaluates the Chi Square PDF; PDF parameter A = 4 X PDF CDF CDF_INV 8.90289 0.0259557 0.0635732 0.814993 1.60868 0.179924 0.807231 6.08666 6.34767 0.066401 0.174645 1.50726 6.28985 0.0677262 0.178523 1.52908 2.01285 0.183936 0.733395 5.20808 1.39859 0.173752 0.84444 6.65036 4.83192 0.10785 0.304983 2.22192 0.4003 0.0819222 0.982452 11.9737 5.58849 0.0854495 0.23206 1.82481 2.08457 0.18378 0.720207 5.07396 CHI_SQUARE_SAMPLE_TEST(): CHI_SQUARE_MEAN() computes the Chi Square mean; CHI_SQUARE_SAMPLE() samples the Chi Square distribution; CHI_SQUARE_VARIANCE() computes the Chi Square variance. PDF parameter A = 10 PDF mean = 10 PDF variance = 20 Sample size = 1000 Sample mean = 9.96763 Sample variance = 20.3929 Sample maximum = 30.3859 Sample minimum = 1.43707 CHI_SQUARE_NONCENTRAL_SAMPLE_TEST(): CHI_SQUARE_NONCENTRAL_MEAN() computes the Chi Square Noncentral mean. CHI_SQUARE_NONCENTRAL_SAMPLE() samples the Chi Square Noncentral PDF. CHI_SQUARE_NONCENTRAL_VARIANCE() computes the Chi Square Noncentral variance. PDF parameter A = 3 PDF parameter B = 2 PDF mean = 5 PDF variance = 14 Sample size = 1000 Sample mean = 5.15389 Sample variance = 14.2205 Sample maximum = 24.3119 Sample minimum = 0.0110982 CIRCULAR_NORMAL_01_SAMPLE_TEST(): CIRCULAR_NORMAL_01_MEAN() computes the Circular Normal 01 mean; CIRCULAR_NORMAL_01_SAMPLE() samples the Circular Normal 01 distribution; CIRCULAR_NORMAL_01_VARIANCE() computes the Circular Normal 01 variance. PDF means = 0 0 PDF variances = 1 1 Sample size = 1000 Sample mean = 0.0459601 0.0158355 Sample variance = 1.12188 1.00064 Sample maximum = 3.35596 3.27255 Sample minimum = -3.8199 -2.7331 CIRCULAR_NORMAL_SAMPLE_TEST(): CIRCULAR_NORMAL_MEAN() computes the Circular Normal mean; CIRCULAR_NORMAL_SAMPLE() samples the Circular Normal distribution; CIRCULAR_NORMAL_VARIANCE() computes the Circular Normal variance. PDF means = 1 5 PDF variances = 0.5625 0.5625 Sample size = 1000 Sample mean = 1.02621 5.03291 Sample variance = 0.563366 0.566156 Sample maximum = 3.42789 7.80635 Sample minimum = -1.53294 3.00665 COSINE_CDF_TEST() COSINE_CDF() evaluates the Cosine CDF. COSINE_CDF_INV() inverts the Cosine CDF. COSINE_PDF() evaluates the Cosine PDF. PDF parameter A = 2 PDF parameter B = 1 X PDF CDF CDF_INV 1.33962 0.125694 0.297269 1.33962 -0.405282 -0.117926 0.0103056 -0.405282 1.40942 0.132197 0.317381 1.40942 1.25794 0.117309 0.274338 1.25794 3.21184 0.05591 0.841882 3.21184 3.23716 0.0521209 0.847278 3.23716 2.18101 0.156555 0.55746 2.18101 1.79215 0.155729 0.434076 1.79215 3.32996 0.0379606 0.866232 3.32996 2.26461 0.153615 0.583739 2.26461 COSINE_SAMPLE_TEST(): COSINE_MEAN() computes the Cosine mean; COSINE_SAMPLE() samples the Cosine distribution; COSINE_VARIANCE() computes the Cosine variance. PDF parameter A = 2 PDF parameter B = 1 PDF mean = 2 PDF variance = 1.28987 Sample size = 1000 Sample mean = 2.05595 Sample variance = 1.26315 Sample maximum = 4.84707 Sample minimum = -0.822525 coupon_complete_pdf_test(): coupon_complete_pdf() evaluates the Coupon Complete PDF. Number of coupon types is 2 BOX_NUM PDF CDF 1 0.000000 0.000000 2 0.500000 0.500000 3 0.250000 0.750000 4 0.125000 0.875000 5 0.062500 0.937500 6 0.031250 0.968750 7 0.015625 0.984375 8 0.007812 0.992188 9 0.003906 0.996094 10 0.001953 0.998047 11 0.000977 0.999023 12 0.000488 0.999512 13 0.000244 0.999756 14 0.000122 0.999878 15 0.000061 0.999939 16 0.000031 0.999969 17 0.000015 0.999985 18 0.000008 0.999992 19 0.000004 0.999996 20 0.000002 0.999998 Number of coupon types is 3 BOX_NUM PDF CDF 1 0.000000 0.000000 2 0.000000 0.000000 3 0.222222 0.222222 4 0.222222 0.444444 5 0.172840 0.617284 6 0.123457 0.740741 7 0.085048 0.825789 8 0.057613 0.883402 9 0.038714 0.922116 10 0.025911 0.948026 11 0.017308 0.965334 12 0.011550 0.976884 13 0.007704 0.984587 14 0.005137 0.989724 15 0.003425 0.993149 16 0.002284 0.995433 17 0.001522 0.996955 18 0.001015 0.997970 19 0.000677 0.998647 20 0.000451 0.999098 Number of coupon types is 4 BOX_NUM PDF CDF 1 0.000000 0.000000 2 0.000000 0.000000 3 0.000000 0.000000 4 0.093750 0.093750 5 0.140625 0.234375 6 0.146484 0.380859 7 0.131836 0.512695 8 0.110229 0.622925 9 0.088440 0.711365 10 0.069237 0.780602 11 0.053387 0.833988 12 0.040771 0.874759 13 0.030944 0.905703 14 0.023391 0.929094 15 0.017635 0.946729 16 0.013272 0.960001 17 0.009977 0.969978 18 0.007494 0.977472 19 0.005626 0.983098 20 0.004223 0.987321 coupon_sample_test(): coupon_sample() samples the coupon PDF. Number of coupon types is 5 Expected wait is about 8.047190 1 8 2 16 3 6 4 7 5 7 6 13 7 16 8 9 9 17 10 10 Average wait was 10.900000 Number of coupon types is 10 Expected wait is about 23.025851 1 19 2 25 3 15 4 27 5 46 6 17 7 29 8 34 9 30 10 19 Average wait was 26.100000 Number of coupon types is 15 Expected wait is about 40.620753 1 49 2 57 3 51 4 39 5 30 6 58 7 54 8 38 9 55 10 68 Average wait was 49.900000 Number of coupon types is 20 Expected wait is about 59.914645 1 55 2 83 3 56 4 92 5 40 6 64 7 73 8 65 9 65 10 106 Average wait was 69.900000 Number of coupon types is 25 Expected wait is about 80.471896 1 86 2 101 3 61 4 60 5 125 6 178 7 129 8 97 9 142 10 141 Average wait was 112.000000 DERANGED_CDF_TEST(): DERANGED_CDF() evaluates the Deranged CDF; DERANGED_CDF_INV() inverts the Deranged CDF. DERANGED_PDF() evaluates the Deranged PDF; PDF parameter A = 7 X PDF CDF CDF_INV a = 7 0 0.367857 0.367857 0 DERANGED_SAMPLE_TEST(): DERANGED_MEAN() computes the Deranged mean. DERANGED_VARIANCE() computes the Deranged variance. DERANGED_SAMPLE() samples the Deranged distribution. PDF parameter A = 7 PDF mean = 1 PDF variance = 1 Sample size = 1000 Sample mean = 1.043000 Sample variance = 1.080231 Sample maximum = 7 Sample minimum = 0 DIPOLE_CDF_TEST(): DIPOLE_CDF() evaluates the Dipole CDF. DIPOLE_CDF_INV() inverts the Dipole CDF. DIPOLE_PDF() evaluates the Dipole PDF. PDF parameter A = 0 PDF parameter B = 1 X PDF CDF CDF_INV 0.252169 0.631348 0.654098 0.252197 1.61089 0.0429043 0.965794 1.61035 0.105894 0.636437 0.566915 0.105957 0.296146 0.627058 0.678313 0.296143 0.149399 0.635914 0.593723 0.149414 0.668308 0.501953 0.834579 0.668457 0.921231 0.351591 0.895578 0.920898 0.392472 0.610615 0.727301 0.392578 -0.102901 0.636457 0.434949 -0.103027 0.331247 0.622278 0.696832 0.331055 PDF parameter A = 0.785398 PDF parameter B = 0.5 X PDF CDF CDF_INV -0.0642288 0.318301 0.400333 -0.0644531 0.765964 0.248996 0.657907 0.765625 1.95537 0.0566884 0.833026 1.95605 2.25577 0.0427904 0.854107 2.25684 0.780541 0.245769 0.661514 0.780273 0.743083 0.253986 0.652151 0.743164 -2.91445 0.0312692 0.0968294 -2.91602 -0.347977 0.31218 0.322425 -0.347656 0.425006 0.306068 0.560518 0.424805 0.257446 0.316271 0.505575 0.257324 PDF parameter A = 1.5708 PDF parameter B = 0 X PDF CDF CDF_INV 3.25658 0.0274279 0.905166 3.25781 -0.966192 0.164627 0.255473 -0.966797 0.444155 0.265862 0.633048 0.444336 -2.5694 0.0418729 0.118143 -2.56934 -1.96939 0.0652475 0.149556 -1.9707 0.0768749 0.31644 0.524422 0.0771484 0.490601 0.256559 0.645181 0.490234 0.963417 0.165084 0.74407 0.962891 -1.8251 0.0734957 0.15955 -1.82422 1.56757 0.0920696 0.81925 1.56787 DIPOLE_SAMPLE_TEST(): DIPOLE_SAMPLE() samples the Dipole distribution. PDF parameter A = 0 PDF parameter B = 1 Sample size = 1000 Sample mean = 0.0183563 Sample variance = 0.7274 Sample maximum = 5.19875 Sample minimum = -3.96986 PDF parameter A = 0.785398 PDF parameter B = 0.5 Sample size = 1000 Sample mean = 4.24786 Sample variance = 25981.7 Sample maximum = 5046.98 Sample minimum = -554.794 PDF parameter A = 1.5708 PDF parameter B = 0 Sample size = 1000 Sample mean = -23.7599 Sample variance = 639481 Sample maximum = 714.507 Sample minimum = -25228.3 DIRICHLET_PDF_TEST(): DIRICHLET_PDF() evaluates the Dirichlet PDF. Number of components N = 3 PDF parameters A: 1: 0.25 2: 0.5 3: 1.25 PDF arguments X: 1: 0.5 2: 0.125 3: 0.375 PDF value = 0.63907 DIRICHLET_SAMPLE_TEST(): DIRICHLET_SAMPLE() samples the Dirichlet distribution; DIRICHLET_MEAN() computes the Dirichlet mean; DIRICHLET_VARIANCE() computes the Dirichlet variance. Number of components N = 3 PDF parameters A: 1: 0.25 2: 0.5 3: 1.25 PDF mean, variance: 1 0.125000 0.036458 2 0.250000 0.062500 3 0.625000 0.078125 Second moment matrix: Col: 1 2 3 Row 1 : 0.0520833 0.0208333 0.0520833 2 : 0.0208333 0.125 0.104167 3 : 0.0520833 0.104167 0.46875 Sample size = 1000 Observed Min, Max, Mean, Variance: 1 2.77711e-11 0.966409 0.129333 0.037016 2 1.36235e-08 0.962069 0.260269 0.0670817 3 0.000902807 0.999848 0.610398 0.08331 DIRICHLET_MIX_PDF_TEST(): DIRICHLET_MIX_PDF() evaluates the Dirichlet Mix PDF. Number of elements ELEM_NUM = 3 Number of components COMP_NUM = 2 PDF parameters A(ELEM,COMP): Col: 1 2 Row 1 : 0.25 1.5 2 : 0.5 0.5 3 : 1.25 2 Component weights: 1: 1 2: 2 PDF value = 2.12288 DIRICHLET_MIX_SAMPLE_TEST(): DIRICHLET_MIX_SAMPLE() samples the Dirichlet Mix distribution; DIRICHLET_MIX_MEAN() computes the Dirichlet Mix mean; Number of elements ELEM_NUM = 3 Number of components COMP_NUM = 2 PDF parameters A(ELEM,COMP): Col: 1 2 Row 1 : 0.25 1.5 2 : 0.5 0.5 3 : 1.25 2 Component weights: 1: 1 2: 2 PDF mean: 1: 0.291667 2: 0.166667 3: 0.541667 Sample size = 1000 Observed Min, Max, Mean, Variance: 1 9.2958e-14 0.972624 0.295243 0.0531858 2 2.68672e-07 0.977902 0.158954 0.0360106 3 0.00545472 0.999988 0.545802 0.061151 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: 1 1 2 2 3 6 4 2 5 4 6 1 X PDF CDF CDF_INV 3 0.375 0.5625 3 5 0.25 0.9375 5 3 0.375 0.5625 3 4 0.125 0.6875 4 3 0.375 0.5625 3 3 0.375 0.5625 3 4 0.125 0.6875 4 3 0.375 0.5625 3 5 0.25 0.9375 5 5 0.25 0.9375 5 DISCRETE_SAMPLE_TEST(): DISCRETE_MEAN() computes the Discrete mean; DISCRETE_SAMPLE() samples the Discrete distribution; DISCRETE_VARIANCE() computes the Discrete variance. PDF parameter A = 6 PDF parameters B: 1 1 2 2 3 6 4 2 5 4 6 1 PDF mean = 3.5625 PDF variance = 1.74609 Sample size = 1000 Sample mean = 3.598000 Sample variance = 1.726122 Sample maximum = 6 Sample minimum = 1 DISK_SAMPLE_TEST(): DISK_MEAN() returns the Disk mean. DISK_SAMPLE() samples the Disk distribution. DISK_VARIANCE() returns the Disk variance. X coordinate of center is A = 10 Y coordinate of center is B = 4 Radius is C = 5 Disk mean = 10 4 Disk variance = 12.5 Sample size = 1000 Sample mean = 9.93769 4.15485 Sample variance = 12.6014 Sample maximum = 14.9588 8.97016 Sample minimum = 5.01767 -0.955745 empirical_discrete_cdf_test(): empirical_discrete_cdf() evaluates the Empirical Discrete CDF; empirical_discrete_cdf_inv() inverts the Empirical Discrete CDF. empirical_discrete_pdf evaluates the Empirical Discrete PDF; PDF parameter A = 6 PDF parameter B: 1: 1 2: 1 3: 3 4: 2 5: 1 6: 2 PDF parameter C: 1: 0 2: 1 3: 2 4: 4.5 5: 6 6: 10 X PDF CDF CDF_INV 4.5 0.2 0.7 4.5 2 0.3 0.5 2 0 0.1 0.1 0 2 0.3 0.5 2 0 0.1 0.1 0 1 0.1 0.2 1 0 0.1 0.1 0 4.5 0.2 0.7 4.5 6 0.1 0.8 6 0 0.1 0.1 0 EMPIRICAL_DISCRETE_SAMPLE_TEST(): EMPIRICAL_DISCRETE_MEAN() computes the Empirical Discrete mean; EMPIRICAL_DISCRETE_SAMPLE() samples the Empirical Discrete distribution; EMPIRICAL_DISCRETE_VARIANCE computes the Empirical Discrete variance. PDF parameter A = 6 PDF parameter B: 1: 1 2: 1 3: 3 4: 2 5: 1 6: 2 PDF parameter C: 1: 0 2: 1 3: 2 4: 4.5 5: 6 6: 10 PDF mean = 4.2 PDF variance = 11.31 Sample size = 1000 Sample mean = 4.169 Sample variance = 11.2157 Sample maximum = 10 Sample minimum = 0 ENGLISH_LETTER_CDF_TEST(): ENGLISH_LETTER_CDF() evaluates the English Letter CDF; ENGLISH_LETTER_CDF_INV() inverts the English Letter CDF. ENGLISH_LETTER_PDF() evaluates the English Letter PDF; C PDF CDF CDF_INV 'r' 0.059870 0.763220 'r' 't' 0.090560 0.917050 't' 'i' 0.069660 0.466990 'i' 'y' 0.019740 0.999260 'y' 'd' 0.042530 0.166940 'd' 's' 0.063270 0.826490 's' 'e' 0.127020 0.293960 'e' 'd' 0.042530 0.166940 'd' 'w' 0.023610 0.978020 'w' 'e' 0.127020 0.293960 'e' ENGLISH_SENTENCE_LENGTH_CDF_TEST(): ENGLISH_SENTENCE_LENGTH_CDF() evaluates the English Sentence Length CDF; ENGLISH_SENTENCE_LENGTH_CDF_INV() inverts the English Sentence Length CDF. ENGLISH_SENTENCE_LENGTH_PDF() evaluates the English Sentence Length PDF; X PDF CDF CDF_INV 12 0.0379681 0.341262 12 7 0.0352418 0.16371 7 26 0.0218306 0.769034 26 5 0.0305008 0.0965039 5 15 0.0352618 0.450896 15 12 0.0379681 0.341262 12 30 0.0155962 0.840951 30 25 0.0209085 0.747204 25 18 0.0331269 0.553935 18 14 0.0375972 0.415634 14 ENGLISH_SENTENCE_LENGTH_SAMPLE_TEST(): ENGLISH_SENTENCE_LENGTH_MEAN() computes the English Sentence Length mean; ENGLISH_SENTENCE_LENGTH_SAMPLE() samples the English Sentence Length distribution; ENGLISH_SENTENCE_LENGTH_VARIANCE() computes the English Sentence Length variance. PDF mean = 19.1147 PDF variance = 147.443 Sample size = 1000 Sample mean = 19.277 Sample variance = 156.441 Sample maximum = 72 Sample minimum = 1 ENGLISH_WORD_LENGTH_CDF_TEST(): ENGLISH_WORD_LENGTH_CDF() evaluates the English Word Length CDF; ENGLISH_WORD_LENGTH_CDF_INV() inverts the English Word Length CDF. ENGLISH_WORD_LENGTH_PDF() evaluates the English Word Length PDF; X PDF CDF CDF_INV 2 0.169755 0.201356 2 13 0.00483014 0.99511 13 6 0.0852426 0.763833 6 8 0.0562317 0.897307 8 2 0.169755 0.201356 2 2 0.169755 0.201356 2 3 0.211926 0.413282 3 6 0.0852426 0.763833 6 5 0.108523 0.67859 5 8 0.0562317 0.897307 8 ENGLISH_WORD_LENGTH_SAMPLE_TEST(): ENGLISH_WORD_LENGTH_MEAN() computes the English Word Length mean; ENGLISH_WORD_LENGTH_SAMPLE() samples the English Word Length distribution; ENGLISH_WORD_LENGTH_VARIANCE() computes the English Word Length variance. PDF mean = 4.73912 PDF variance = 7.05635 Sample size = 1000 Sample mean = 4.666 Sample variance = 6.88133 Sample maximum = 15 Sample minimum = 1 ERLANG_CDF_TEST(): ERLANG_CDF() evaluates the Erlang CDF. ERLANG_CDF_INV() inverts the Erlang CDF. ERLANG_PDF() evaluates the Erlang PDF. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 4.43237 0.132354 0.247056 4.43164 13.5965 0.0182426 0.95009 13.5938 3.91923 0.123741 0.181086 3.91992 9.51576 0.0641436 0.797302 9.51562 7.63641 0.0996939 0.644216 7.63672 3.25787 0.103036 0.105479 3.25781 4.86311 0.135173 0.304805 4.86328 4.33685 0.13121 0.234466 4.33691 3.56199 0.113948 0.138534 3.5625 7.3391 0.10554 0.613705 7.33984 ERLANG_SAMPLE_TEST(): ERLANG_MEAN() computes the Erlang mean; ERLANG_SAMPLE() samples the Erlang distribution; ERLANG_VARIANCE() computes the Erlang variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 7 PDF variance = 12 Sample size = 1000 Sample mean = 7.04508 Sample variance = 11.6811 Sample maximum = 20.906 Sample minimum = 1.26341 EXPONENTIAL_CDF_TEST(): EXPONENTIAL_CDF() evaluates the Exponential CDF. EXPONENTIAL_CDF_INV() inverts the Exponential CDF. EXPONENTIAL_PDF() evaluates the Exponential PDF. PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV 3.10519 0.174515 0.650969 3.10519 1.41675 0.405951 0.188098 1.41675 2.35045 0.254521 0.490958 2.35045 2.02455 0.299566 0.400869 2.02455 4.89079 0.0714653 0.857069 4.89079 1.43719 0.401824 0.196352 1.43719 3.95905 0.113873 0.772254 3.95905 2.1753 0.277816 0.444368 2.1753 2.57055 0.227998 0.544005 2.57055 3.41026 0.149826 0.700348 3.41026 EXPONENTIAL_SAMPLE_TEST(): EXPONENTIAL_MEAN() computes the Exponential mean; EXPONENTIAL_SAMPLE() samples the Exponential distribution; EXPONENTIAL_VARIANCE() computes the Exponential variance. PDF parameter A = 1 PDF parameter B = 10 PDF mean = 11 PDF variance = 100 Sample size = 1000 Sample mean = 10.3271 Sample variance = 78.1316 Sample maximum = 76.6591 Sample minimum = 1.01209 EXPONENTIAL_01_CDF_TEST(): EXPONENTIAL_01_CDF() evaluates the Exponential 01 CDF. EXPONENTIAL_01_CDF_INV() inverts the Exponential 01 CDF. EXPONENTIAL_01_PDF() evaluates the Exponential 01 PDF. X PDF CDF CDF_INV 0.320895 0.7255 0.2745 0.320895 1.20061 0.301011 0.698989 1.20061 0.749376 0.472661 0.527339 0.749376 0.0240572 0.97623 0.0237702 0.0240572 0.329254 0.71946 0.28054 0.329254 0.0122691 0.987806 0.0121942 0.0122691 2.2191 0.108707 0.891293 2.2191 0.436401 0.646359 0.353641 0.436401 1.69034 0.184456 0.815544 1.69034 2.15048 0.116428 0.883572 2.15048 EXPONENTIAL_01_SAMPLE_TEST(): EXPONENTIAL_01_MEAN() computes the Exponential 01 mean; EXPONENTIAL_01_SAMPLE() samples the Exponential 01 distribution; EXPONENTIAL_01_VARIANCE() computes the Exponential 01 variance. PDF mean = 1 PDF variance = 1 Sample size = 1000 Sample mean = 0.991744 Sample variance = 0.933559 Sample maximum = 6.38785 Sample minimum = 0.00141154 EXTREME_VALUES_CDF_TEST(): EXTREME_VALUES_CDF() evaluates the Extreme Values CDF; EXTREME_VALUES_CDF_INV() inverts the Extreme Values CDF. EXTREME_VALUES_PDF() evaluates the Extreme Values PDF; PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 5.89006 0.0693398 0.760761 5.89006 8.85817 0.0306128 0.903331 8.85817 6.62571 0.0575853 0.80737 6.62571 5.783 0.0711488 0.75324 5.783 2.85837 0.118138 0.471815 2.85837 6.85279 0.0542266 0.820062 6.85279 4.59492 0.0921214 0.656349 4.59492 6.71272 0.0562823 0.812323 6.71272 1.57071 0.121316 0.315422 1.57071 3.43295 0.111191 0.537816 3.43295 EXTREME_VALUES_SAMPLE_TEST(): EXTREME_VALUES_MEAN() computes the Extreme Values mean; EXTREME_VALUES_SAMPLE() samples the Extreme Values distribution; EXTREME_VALUES_VARIANCE() computes the Extreme Values variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 3.73165 PDF variance = 14.8044 Sample size = 1000 Sample mean = 3.71995 Sample variance = 15.5325 Sample maximum = 29.2947 Sample minimum = -4.4146 F_CDF_TEST(): F_CDF() evaluates the F CDF. F_PDF() evaluates the F PDF. PDF parameter M = 1 PDF parameter N = 1 X M N PDF CDF 7.40959 1 1 0.0139052 0.224131 16.9287 1 1 0.00431508 0.151785 22.4505 1 1 0.00286475 0.132416 1.23449 1 1 0.128211 0.466534 0.826106 1 1 0.191781 0.530358 25.2679 1 1 0.00241068 0.125015 0.3783 1 1 0.375482 0.648955 568.338 1 1 2.34518e-05 0.0266884 6.18196 1 1 0.0178256 0.243442 0.854854 1 1 0.185607 0.524934 f_sample_test(): f_mean() computes the F mean; f_sample() samples the F distribution; f_variance() computes the F variance. PDF parameter M = 8 PDF parameter N = 6 PDF mean = 1.5 PDF variance = 3.375 Sample size = 1000 Sample mean = 1.41174 Sample variance = 2.31321 Sample maximum = 25.8311 Sample minimum = 0.0556026 FERMI_DIRAC_SAMPLE_TEST(): FERMI_DIRAC_SAMPLE() samples the Fermi Dirac distribution. U = 1 V = 1 SAMPLE_NUM = 10000 Sample mean = 0.602401 Sample variance = 0.183212 Maximum value = 2.63334 Minimum value = 0.000194993 U = 2 V = 1 SAMPLE_NUM = 10000 Sample mean = 1.05011 Sample variance = 0.434325 Maximum value = 3.61075 Minimum value = 5.95277e-05 U = 4 V = 1 SAMPLE_NUM = 10000 Sample mean = 2.02628 Sample variance = 1.45077 Maximum value = 5.52055 Minimum value = 0.000111415 U = 8 V = 1 SAMPLE_NUM = 10000 Sample mean = 4.01497 Sample variance = 5.37993 Maximum value = 9.46204 Minimum value = 0.000634794 U = 16 V = 1 SAMPLE_NUM = 10000 Sample mean = 7.9627 Sample variance = 21.9378 Maximum value = 17.2055 Minimum value = 0.00153086 U = 32 V = 1 SAMPLE_NUM = 10000 Sample mean = 16.0543 Sample variance = 84.8075 Maximum value = 33.6158 Minimum value = 0.00371096 U = 1 V = 0.25 SAMPLE_NUM = 10000 Sample mean = 0.507601 Sample variance = 0.089863 Maximum value = 1.35023 Minimum value = 4.81216e-05 FISHER_PDF_TEST(): FISHER_PDF() evaluates the Fisher PDF. PDF parameters: Concentration parameter KAPPA = 0.000000 Direction MU(1:3) = 1.000000 0.000000 0.000000 X PDF -0.539254 -0.045334 0.840922 0.0795775 -0.166664 -0.926807 -0.336528 0.0795775 -0.382283 -0.916396 0.118651 0.0795775 -0.094577 0.995372 -0.017023 0.0795775 -0.645876 -0.091627 -0.757924 0.0795775 -0.022169 -0.519246 -0.854337 0.0795775 0.766490 0.580981 -0.273778 0.0795775 0.506613 -0.842249 0.184281 0.0795775 -0.462914 -0.831622 0.306783 0.0795775 0.125077 -0.975805 0.179334 0.0795775 PDF parameters: Concentration parameter KAPPA = 0.500000 Direction MU(1:3) = 1.000000 0.000000 0.000000 X PDF -0.550216 0.052469 -0.833373 0.0579916 -0.553404 0.146235 0.819975 0.0578992 -6.587227 0.000000 0.000000 0.0535062 -0.595203 -0.755235 0.274505 0.0567017 -4.286475 -0.000000 0.000000 0.0533536 -0.941361 0.084572 -0.326629 0.0476902 -9.317641 0.000000 -0.000000 0.0535615 -0.845487 0.532354 0.041856 0.050032 -1.284929 -0.000000 -0.000000 0.0499973 -2.934994 -0.000000 0.000000 0.053044 PDF parameters: Concentration parameter KAPPA = 10.000000 Direction MU(1:3) = 1.000000 0.000000 0.000000 X PDF 0.760564 -0.645726 -0.067672 0.145199 0.860982 0.322702 -0.393158 0.396345 0.825588 0.524152 -0.208970 0.278202 0.904696 0.055065 -0.422485 0.613647 0.808615 -0.569488 -0.147730 0.234773 0.982082 0.185004 -0.035905 1.33046 0.929029 0.143502 -0.341047 0.7827 0.936226 0.300556 -0.182064 0.841111 0.955509 0.093047 -0.279903 1.01999 0.878141 -0.359703 -0.315409 0.470534 FISK_CDF_TEST(): FISK_CDF() evaluates the Fisk CDF; FISK_CDF_INV() inverts the Fisk CDF. FISK_PDF() evaluates the Fisk PDF; PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV 3.25899 0.321171 0.590327 3.25899 10.3582 0.00306902 0.990333 10.3582 3.03076 0.369127 0.511444 3.03076 2.7468 0.412131 0.399852 2.7468 7.31911 0.0141409 0.96927 7.31911 1.4123 0.0626435 0.00868466 1.4123 4.36494 0.127865 0.826466 4.36494 3.19366 0.335407 0.568877 3.19366 6.02319 0.0333527 0.94063 6.02319 1.49238 0.0882609 0.0147021 1.49238 FISK_SAMPLE_TEST(): FISK_MEAN() computes the Fisk mean; FISK_SAMPLE() samples the Fisk distribution; FISK_VARIANCE() computes the Fisk variance. PDF parameter A = 1.000000 PDF parameter B = 2.000000 PDF parameter C = 3.000000 PDF mean = 3.418399 PDF variance = 3.824942 Sample size = 1000 Sample mean = 3.315468 Sample variance = 2.165261 Sample maximum = 17.879430 Sample minimum = 1.106459 FOLDED_NORMAL_CDF_TEST(): FOLDED_NORMAL_CDF() evaluates the Folded Normal CDF. FOLDED_NORMAL_CDF_INV() inverts the Folded Normal CDF. FOLDED_NORMAL_PDF() evaluates the Folded Normal PDF. PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 3.0674 0.156757 0.593407 3.06719 0.820192 0.20857 0.173468 0.820074 1.49501 0.198574 0.311153 1.49548 2.89342 0.162372 0.565644 2.89322 0.190207 0.212728 0.0404925 0.190219 4.25725 0.115302 0.755599 4.25773 0.724505 0.209531 0.153464 0.724539 2.66271 0.169516 0.527353 2.66257 1.74509 0.193509 0.360194 1.74523 2.56775 0.172345 0.51112 2.56817 FOLDED_NORMAL_SAMPLE_TEST(): FOLDED_NORMAL_MEAN() computes the Folded Normal mean; FOLDED_NORMAL_SAMPLE() samples the Folded Normal distribution; FOLDED_NORMAL_VARIANCE() computes the Folded Normal variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2.90672 PDF variance = 4.55099 Sample size = 1000 Sample mean = 2.96334 Sample variance = 4.75113 Sample maximum = 12.1667 Sample minimum = 0.0107872 FRECHET_CDF_TEST(): FRECHET_CDF() evaluates the Frechet CDF; FRECHET_CDF_INV() inverts the Frechet CDF. FRECHET_PDF() evaluates the Frechet PDF; PDF parameter ALPHA = 3 X PDF CDF CDF_INV 1.33442 0.621129 0.656491 1.33442 1.23548 0.757677 0.588452 1.23548 0.809612 1.06081 0.151923 0.809612 1.85908 0.21495 0.855872 1.85908 0.873064 1.14905 0.222536 0.873064 0.961642 1.13947 0.324815 0.961642 1.01335 1.08825 0.382513 1.01335 0.832111 1.10312 0.17629 0.832111 0.813393 1.06881 0.155949 0.813393 2.94173 0.0385166 0.96148 2.94173 FRECHET_SAMPLE_TEST(): FRECHET_MEAN() computes the Frechet mean; FRECHET_SAMPLE() samples the Frechet distribution; FRECHET_VARIANCE() computes the Frechet variance. PDF parameter ALPHA = 3 PDF mean = 1.35412 PDF variance = 0.845303 Sample size = 1000 Sample mean = 1.36016 Sample variance = 0.712144 Sample maximum = 10.0736 Sample minimum = 0.530033 gamma_cdf_test(): gamma_cdf() evaluates the Gamma CDF. gamma_pdf() evaluates the Gamma PDF. PDF parameter A = 1 PDF parameter B = 1.5 PDF parameter C = 3 X PDF CDF 7.74842 0.0750297 0.826303 2.20136 0.0959876 0.0475535 3.91454 0.180298 0.307906 5.31371 0.1554 0.548418 6.42048 0.117323 0.699663 5.59123 0.146304 0.590297 4.48132 0.176295 0.40949 14.6421 0.00309503 0.994224 8.7849 0.0500314 0.89046 6.75432 0.105837 0.736903 5.59141 0.146298 0.590323 GAMMA_SAMPLE_TEST(): GAMMA_MEAN() computes the Gamma mean; GAMMA_SAMPLE() samples the Gamma distribution; GAMMA_VARIANCE() computes the Gamma variance. TEST NUMBER: 1 PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 2 PDF mean = 7 PDF variance = 18 Sample size = 1000 Sample mean = 7.26746 Sample variance = 18.9677 Sample maximum = 28.6824 Sample minimum = 1.10544 TEST NUMBER: 2 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 = 2.25654 Sample variance = 0.15453 Sample maximum = 5.41158 Sample minimum = 2 GENLOGISTIC_CDF_TEST(): GENLOGISTIC_PDF() evaluates the Genlogistic PDF. GENLOGISTIC_CDF() evaluates the Genlogistic CDF; GENLOGISTIC_CDF_INV() inverts the Genlogistic CDF. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 X PDF CDF CDF_INV -0.0260049 0.0492772 0.0525195 -0.0260049 7.96051 0.0409203 0.913014 7.96051 6.04007 0.0885573 0.792826 6.04007 6.52593 0.0741051 0.832285 6.52593 5.67139 0.100298 0.758028 5.67139 1.58788 0.120485 0.188094 1.58788 2.16013 0.141849 0.263476 2.16013 1.84505 0.130915 0.220444 1.84505 2.08209 0.13936 0.252502 2.08209 7.94894 0.0411293 0.912539 7.94894 GENLOGISTIC_SAMPLE_TEST(): GENLOGISTIC_MEAN() computes the Genlogistic mean; GENLOGISTIC_SAMPLE() samples the Genlogistic distribution; GENLOGISTIC_VARIANCE() computes the Genlogistic variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 4 PDF variance = 8.15947 Sample size = 1000 Sample mean = 3.98585 Sample variance = 7.83039 Sample maximum = 19.4637 Sample minimum = -3.10045 GEOMETRIC_CDF_TEST(): GEOMETRIC_CDF ()evaluates the Geometric CDF; GEOMETRIC_CDF_INV() inverts the Geometric CDF. GEOMETRIC_PDF() evaluates the Geometric PDF; PDF parameter A = 0.25 X PDF CDF CDF_INV 2 0.1875 0.4375 3 5 0.0791016 0.762695 6 1 0.25 0.25 2 1 0.25 0.25 2 2 0.1875 0.4375 3 8 0.033371 0.899887 9 3 0.140625 0.578125 4 9 0.0250282 0.924915 10 10 0.0187712 0.943686 11 9 0.0250282 0.924915 10 GEOMETRIC_SAMPLE_TEST(): GEOMETRIC_MEAN() computes the Geometric mean; GEOMETRIC_SAMPLE() samples the Geometric distribution; GEOMETRIC_VARIANCE() computes the Geometric variance. PDF parameter A = 0.25 PDF mean = 4 PDF variance = 12 Sample size = 1000 Sample mean = 4.037000 Sample variance = 11.809440 Sample maximum = 27 Sample minimum = 1 GOMPERTZ_CDF_TEST(): GOMPERTZ_CDF() evaluates the Gompertz CDF; GOMPERTZ_CDF_INV() inverts the Gompertz CDF. GOMPERTZ_PDF() evaluates the Gompertz PDF; PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 0.537697 0.616635 0.858406 0.537697 0.173213 1.94751 0.424273 0.173213 0.685804 0.346425 0.928214 0.685804 0.28946 1.40162 0.617728 0.28946 0.0759418 2.50258 0.208581 0.0759418 0.0730455 2.52052 0.201307 0.0730455 0.0526924 2.64888 0.148707 0.0526924 0.588648 0.509657 0.887032 0.588648 0.185005 1.88641 0.446876 0.185005 0.419608 0.930957 0.767997 0.419608 GOMPERTZ_SAMPLE_TEST(): GOMPERTZ_SAMPLE() samples the Gompertz distribution; PDF parameter A = 2 PDF parameter B = 3 Sample size = 1000 Sample mean = 0.290312 Sample variance = 0.0628141 Sample maximum = 1.55024 Sample minimum = 8.73677e-06 GUMBEL_CDF_TEST(): GUMBEL_CDF() evaluates the Gumbel CDF. GUMBEL_CDF_INV() inverts the Gumbel CDF. GUMBEL_PDF() evaluates the Gumbel PDF. X PDF CDF CDF_INV 2.89456 0.0523461 0.946179 2.89456 1.09683 0.239128 0.716104 1.09683 -0.510835 0.314791 0.188873 -0.510835 0.670461 0.306685 0.599612 0.670461 1.9312 0.125409 0.865045 1.9312 1.41855 0.190023 0.785005 1.41855 3.52228 0.0286725 0.9709 3.52228 4.0975 0.0163404 0.983523 4.0975 1.01897 0.251594 0.697003 1.01897 0.3691 0.346298 0.500896 0.3691 GUMBEL_SAMPLE_TEST(): GUMBEL_MEAN() computes the Gumbel mean; GUMBEL_SAMPLE() samples the Gumbel distribution; GUMBEL_VARIANCE() computes the Gumbel variance. PDF mean = 0.577216 PDF variance = 1.64493 Sample size = 1000 Sample mean = 0.614741 Sample variance = 1.68018 Sample maximum = 8.6292 Sample minimum = -1.79248 half_normal_cdf_test(): half_normal_cdf() evaluates the Half Normal CDF. half_normal_cdf_inv() inverts the Half Normal CDF. half_normal_pdf() evaluates the Half Normal PDF. PDF parameter A = 0 PDF parameter B = 2 X PDF CDF CDF_INV 0.419247 0.390273 0.166038 0.419247 0.646378 0.378642 0.253448 0.646378 2.882 0.141256 0.850415 2.882 0.0365442 0.398876 0.0145782 0.0365442 1.8715 0.257496 0.650597 1.8715 0.198174 0.396989 0.0789309 0.198174 4.35473 0.0372764 0.970547 4.35473 0.0189333 0.398924 0.00755317 0.0189333 2.34277 0.200887 0.758556 2.34277 2.22357 0.215032 0.733769 2.22357 HALF_NORMAL_SAMPLE_TEST(): HALF_NORMAL_MEAN() computes the Half Normal mean; HALF_NORMAL_SAMPLE() samples the Half Normal distribution; HALF_NORMAL_VARIANCE() computes the Half Normal variance. PDF parameter A = 0 PDF parameter B = 10 PDF mean = 7.97885 PDF variance = 36.338 Sample size = 1000 Sample mean = 7.60465 Sample variance = 33.7183 Sample maximum = 34.8216 Sample minimum = 0.0072092 INVERSE_GAUSSIAN_CDF_TEST(): INVERSE_GAUSSIAN_CDF() evaluates the Inverse Gaussian CDF. INVERSE_GAUSSIAN_PDF() evaluates the Inverse Gaussian PDF. PDF parameter A = 5 PDF parameter B = 2 X PDF CDF 5.91692 0.0389774 0.769792 9.16552 0.0188496 0.858059 1.03508 0.291827 0.239086 6.25028 0.0357463 0.782236 31.1427 0.00134946 0.981943 3.00353 0.102783 0.585354 0.767454 0.32987 0.155533 1.34588 0.242979 0.322059 6.63456 0.0324871 0.795332 2.15421 0.153528 0.478644 INVERSE_GAUSSIAN_SAMPLE_TEST(): INVERSE_GAUSSIAN_MEAN() computes the Inverse Gaussian mean; INVERSE_GAUSSIAN_SAMPLE() samples the Inverse Gaussian distribution; INVERSE_GAUSSIAN_VARIANCE() computes the Inverse Gaussian variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 2.66667 Sample size = 1000 Sample mean = 1.97953 Sample variance = 2.54528 Sample maximum = 13.578 Sample minimum = 0.198905 i4_choose_log_test(): i4_choose_log() evaluates log(C(N,K)). N K lcnk elcnk CNK 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 2 0 0 1 1 2 1 0.693147 2 2 2 2 0 1 1 3 0 0 1 1 3 1 1.09861 3 3 3 2 1.09861 3 3 3 3 0 1 1 4 0 0 1 1 4 1 1.38629 4 4 4 2 1.79176 6 6 4 3 1.38629 4 4 4 4 0 1 1 I4_IS_POWER_OF_10_TEST(): I4_IS_POWER_OF_10() reports whether an I4 is a power of 10. I I4_IS_POWER_OF_10(I) 97 0 98 0 99 0 100 1 101 0 102 0 103 0 I4VEC_UNIQUE_COUNT_TEST(): I4VEC_UNIQUE_COUNT() counts unique entries in an I4VEC. Input vector: 1: 13 2: 17 3: 3 4: 18 5: 10 6: 8 7: 3 8: 12 9: 10 10: 10 11: 7 12: 17 13: 7 14: 8 15: 18 16: 19 17: 15 18: 17 19: 18 20: 6 Number of unique entries is 11 HYPERGEOMETRIC_CDF_TEST(): HYPERGEOMETRIC_CDF() evaluates the Hypergeometric CDF. HYPERGEOMETRIC_PDF() evaluates the Hypergeometric PDF. PDF argument X = 7 Total number of balls = 100 Number of white balls = 7 Number of balls taken = 10 PDF value = = 7.49646e-09 CDF value = = 1 HYPERGEOMETRIC_SAMPLE_TEST(): HYPERGEOMETRIC_MEAN() computes the Hypergeometric mean; HYPERGEOMETRIC_SAMPLE() samples the Hypergeometric distribution; HYPERGEOMETRIC_VARIANCE() computes the Hypergeometric variance. PDF parameter N = 10 PDF parameter M = 7 PDF parameter L = 100 PDF mean = 0.7 PDF variance = 0.591818 Sample size = 1000 Sample mean = 0.731 Sample variance = 0.573212 Sample maximum = 4 Sample minimum = 0 laplace_cdf_test(): laplace_cdf() evaluates the Laplace CDF; laplace_cdf_inv() inverts the Laplace CDF. laplace_pdf() evaluates the Laplace PDF; PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV 3.07576 0.0885511 0.822898 3.07576 -1.19365 0.0834823 0.166965 -1.19365 6.12256 0.0193015 0.961397 6.12256 0.488999 0.193632 0.387264 0.488999 0.568417 0.201476 0.402952 0.568417 -0.0506909 0.147838 0.295676 -0.0506909 0.9644 0.245589 0.491179 0.9644 0.960014 0.245051 0.490103 0.960014 -0.148518 0.140781 0.281561 -0.148518 1.89996 0.15941 0.68118 1.89996 LAPLACE_SAMPLE_TEST(): LAPLACE_MEAN() computes the Laplace mean; LAPLACE_SAMPLE() samples the Laplace distribution; LAPLACE_VARIANCE() computes the Laplace variance. PDF parameter A = 1 PDF parameter B = 2 PDF mean = 1 PDF variance = 8 Sample size = 1000 Sample mean = 0.940231 Sample variance = 7.80356 Sample maximum = 12.1404 Sample minimum = -15.6814 LEVY_CDF_TEST(): LEVY_CDF() evaluates the Levy CDF; LEVY_CDF_INV() inverts the Levy CDF. LEVY_PDF() evaluates the Levy PDF; PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV 97.7313 0.000586928 0.885666 97.7313 2.06121 0.201131 0.169808 2.06121 3.03975 0.118616 0.322073 3.03975 21.1888 0.00591899 0.752955 21.1888 25.5105 0.00446352 0.775144 25.5105 17.9157 0.00764393 0.730958 17.9157 3.15619 0.112067 0.335497 3.15619 42.4031 0.00206722 0.826038 42.4031 10.4056 0.0175862 0.644706 10.4056 19.7213 0.00660272 0.743782 19.7213 logistic_cdf_test(): logistic_cdf() evaluates the Logistic CDF; logistic_cdf_inv() inverts the Logistic CDF. logistic_pdf() evaluates the Logistic PDF; PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV -1.1972 0.0937506 0.250002 -1.1972 -1.69962 0.081753 0.205901 -1.69962 1.22316 0.124612 0.527866 1.22316 0.157472 0.119614 0.396214 0.157472 6.14873 0.0328965 0.929193 6.14873 8.66018 0.0103975 0.978754 8.66018 4.22609 0.0692775 0.833834 4.22609 -1.0664 0.0967885 0.262465 -1.0664 0.0110408 0.11766 0.378839 0.0110408 -1.15113 0.0948271 0.254346 -1.15113 logistic_plot_test(): Plot the PDF, CDF, and inverse CDF of logistic distribution; PDF parameter A = 0 PDF parameter B = 1 Graphics saved as "logistic_pdf.png" Graphics saved as "logistic_cdf.png" Graphics saved as "logistic_icdf.png" LOGISTIC_SAMPLE_TEST(): LOGISTIC_MEAN() computes the Logistic mean; LOGISTIC_SAMPLE() samples the Logistic distribution; LOGISTIC_VARIANCE() computes the Logistic variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 29.6088 Sample size = 1000 Sample mean = 1.94369 Sample variance = 31.4311 Sample maximum = 21.6275 Sample minimum = -24.1925 LOG_NORMAL_CDF_TEST(): LOG_NORMAL_CDF() evaluates the Log Normal CDF; LOG_NORMAL_CDF_INV() inverts the Log Normal CDF. LOG_NORMAL_PDF() evaluates the Log Normal PDF; PDF parameter A = 10 PDF parameter B = 2.25 X PDF CDF CDF_INV 365240 2.22775e-07 0.89401 365240 3856.69 3.40632e-05 0.219343 3856.69 2466.26 4.4777e-05 0.165244 2466.26 1670.63 5.5023e-05 0.125847 1670.63 45782.2 3.67341e-06 0.627477 45782.2 213028 5.00527e-07 0.843398 213028 28211.9 6.24695e-06 0.543795 28211.9 371.888 9.20034e-05 0.0348421 371.888 266845 3.59402e-07 0.866206 266845 306337 2.91937e-07 0.878994 306337 LOG_NORMAL_SAMPLE_TEST(): LOG_NORMAL_MEAN() computes the Log Normal mean; LOG_NORMAL_SAMPLE() samples the Log Normal distribution; LOG_NORMAL_VARIANCE() computes the Log Normal variance. PDF parameter A = 1 PDF parameter B = 2 PDF mean = 20.0855 PDF variance = 21623 Sample size = 1000 Sample mean = 20.0477 Sample variance = 6438.74 Sample maximum = 1698.34 Sample minimum = 0.0121373 LOG_SERIES_CDF_TEST(): LOG_SERIES_CDF() evaluates the Log Series CDF; LOG_SERIES_CDF_INV() inverts the Log Series CDF. LOG_SERIES_PDF() evaluates the Log Series PDF; PDF parameter A = 0.25 X PDF CDF CDF_INV 1 0.869015 0.869015 2 3 0.0181045 0.995746 4 1 0.869015 0.869015 2 1 0.869015 0.869015 2 2 0.108627 0.977642 3 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 LOG_SERIES_SAMPLE_TEST(): LOG_SERIES_MEAN() computes the Log Series mean; LOG_SERIES_VARIANCE() computes the Log Series variance; LOG_SERIES_SAMPLE() samples the Log Series distribution. PDF parameter A = 0.25 PDF mean = 1.15869 PDF variance = 0.202361 Sample size = 1000 Sample mean = 1.154000 Sample variance = 0.190474 Sample maximum = 5 Sample minimum = 1 LOG_UNIFORM_CDF_TEST(): LOG_UNIFORM_CDF() evaluates the Log Uniform CDF; LOG_UNIFORM_CDF_INV() inverts the Log Uniform CDF. LOG_UNIFORM_PDF() evaluates the Log Uniform PDF; PDF parameter A = 2 PDF parameter B = 20 X PDF CDF CDF_INV 2.81087 0.154506 0.14781 2.81087 5.70142 0.0761731 0.454953 5.70142 6.95361 0.062456 0.54118 6.95361 18.2625 0.0237807 0.96053 18.2625 14.8072 0.0293299 0.869444 14.8072 2.6398 0.164518 0.120541 2.6398 2.18864 0.198431 0.0391447 2.18864 7.75715 0.0559864 0.588672 7.75715 2.14188 0.202763 0.029765 2.14188 19.9603 0.0217579 0.999137 19.9603 LOG_UNIFORM_SAMPLE_TEST(): LOG_UNIFORM_MEAN() computes the Log Uniform mean; LOG_UNIFORM_SAMPLE() samples the Log Uniform distribution; LOG_UNIFORM_VARIANCE() computes the Log Uniform variance; PDF parameter A = 2 PDF parameter B = 20 PDF mean = 7.817301 PDF variance = 24.880118 Sample size = 1000 Sample mean = 7.72235 Sample variance = 25.2332 Sample maximum = 19.9726 Sample minimum = 2.00051 LORENTZ_CDF_TEST(): LORENTZ_CDF() evaluates the Lorentz CDF; LORENTZ_CDF_INV() inverts the Lorentz CDF. LORENTZ_PDF() evaluates the Lorentz PDF; X PDF CDF CDF_INV -0.639845 0.225848 0.318817 -0.639845 2.88064 0.0342338 0.893643 2.88064 -12.2659 0.00210172 0.0258936 -12.2659 1.86905 0.0708404 0.843621 1.86905 2.74641 0.0372607 0.888849 2.74641 0.314474 0.289664 0.596983 0.314474 1.20327 0.130036 0.779284 1.20327 8.33468 0.00451716 0.961991 8.33468 -3.25481 0.0274552 0.0948829 -3.25481 29.6307 0.000362136 0.989262 29.6307 lorentz_sample_test(): lorentz_mean() computes the Lorentz mean; lorentz_variance() computes the Lorentz variance; lorentz_sample() samples the Lorentz distribution. PDF mean = 0 PDF variance = Inf Sample size = 1000 Sample mean = 0.769127 Sample variance = 846.769 Sample maximum = 757.299 Sample minimum = -239.987 maxwell_cdf_test(): maxwell_cdf() evaluates the Maxwell CDF. maxwell_cdf_inv() inverts the Maxwell CDF. maxwell_pdf() evaluates the Maxwell PDF. PDF parameter A = 2 X PDF CDF CDF_INV 3.17924 0.284963 0.635193 3.17969 4.93025 0.11615 0.823023 4.92969 3.50312 0.263973 0.679643 3.50293 3.0269 0.290713 0.612503 3.02734 3.0624 0.289638 0.617897 3.0625 2.44392 0.282347 0.514489 2.44434 3.85926 0.230843 0.722932 3.85938 4.60665 0.149138 0.797028 4.60742 1.66333 0.195259 0.354882 1.66309 1.49926 0.169269 0.317558 1.49902 maxwell_sample_test(): MAXWELL_MEAN() computes the Maxwell mean; MAXWELL_VARIANCE() computes the Maxwell variance; MAXWELL_SAMPLE() samples the Maxwell distribution. PDF parameter A = 2 PDF mean = 3.19154 PDF mean = 1.81408 Sample size = 1000 Sample mean = 3.15311 Sample variance = 1.8786 Sample maximum = 9.06074 Sample minimum = 0.206212 MULTINOMIAL_COEF_TEST(): MULTINOMIAL_COEF1() computes multinomial coefficients using the Gamma function; MULTINOMIAL_COEF2() computes multinomial coefficients directly. Line 10 of the BINOMIAL table: 0 10 1 1 1 9 10 10 2 8 45 45 3 7 120 120 4 6 210 210 5 5 252 252 6 4 210 210 7 3 120 120 8 2 45 45 9 1 10 10 10 0 1 1 Level 5 of the TRINOMIAL coefficients: 0 0 5 1 1 0 1 4 5 5 0 2 3 10 10 0 3 2 10 10 0 4 1 5 5 0 5 0 1 1 1 0 4 5 5 1 1 3 20 20 1 2 2 30 30 1 3 1 20 20 1 4 0 5 5 2 0 3 10 10 2 1 2 30 30 2 2 1 30 30 2 3 0 10 10 3 0 2 10 10 3 1 1 20 20 3 2 0 10 10 4 0 1 5 5 4 1 0 5 5 5 0 0 1 1 MULTINOMIAL_PDF_TEST(): MULTINOMIAL_PDF() evaluates the Multinomial PDF. PDF argument X: 0 2 3 PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 0.100000 0.500000 0.400000 PDF value = 0.16 MULTINOMIAL_SAMPLE_TEST(): MULTINOMIAL_MEAN() computes the Multinomial mean; MULTINOMIAL_SAMPLE() samples the Multinomial distribution; MULTINOMIAL_VARIANCE() computes the Multinomial variance; PDF parameter A = 5 PDF parameter B = 3 PDF parameter C = 0.125000 0.500000 0.375000 PDF means and variances: 0.625 0.546875 2.5 1.25 1.875 1.17188 Sample size = 1000 Component Min, Max, Mean, Variance: 1 0 3 0.612 0.580036 2 0 5 2.514 1.2951 3 0 5 1.874 1.20133 multinoulli_pdf_test(): multinoulli_pdf() evaluates the Multinoulli PDF. X pdf(X) 0 0 1 0.11514 2 0.160984 3 0.326186 4 0.244529 5 0.153161 6 0 nakagami_cdf_test(): nakagami_cdf() evaluates the Nakagami CDF; nakagami_pdf() evaluates the Nakagami PDF; X PDF CDF CDF_INV 3.18257 0.586699 0.692394 3.18258 3.2582 0.540746 0.735053 3.2582 3.31623 0.503068 0.765346 3.31623 3.36515 0.470346 0.789159 3.36515 3.40825 0.441184 0.808803 3.40825 3.44721 0.414809 0.82548 3.44721 3.48305 0.390724 0.839911 3.48305 3.5164 0.36858 0.852572 3.5164 3.54772 0.348118 0.863796 3.54772 3.57735 0.329135 0.873828 3.57735 NAKAGAMI_SAMPLE_TEST(): NAKAGAMI_MEAN() computes the Nakagami mean; NAKAGAMI_VARIANCE() computes the Nakagami variance. PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF mean = 2.91874 PDF variance = 0.318446 NEGATIVE_BINOMIAL_CDF_TEST(): NEGATIVE_BINOMIAL_CDF() evaluates the Negative Binomial CDF. NEGATIVE_BINOMIAL_CDF_INV() inverts the Negative Binomial CDF. NEGATIVE_BINOMIAL_PDF() evaluates the Negative Binomial PDF. PDF parameter A = 2 PDF parameter B = 0.25 X PDF CDF CDF_INV 12 0.0387155 0.841618 12 8 0.0778656 0.632919 8 3 0.09375 0.15625 3 8 0.0778656 0.632919 8 9 0.0667419 0.699661 9 5 0.105469 0.367188 5 3 0.09375 0.15625 3 10 0.0563135 0.755975 10 5 0.105469 0.367188 5 6 0.098877 0.466064 6 NEGATIVE_BINOMIAL_SAMPLE_TEST(): NEGATIVE_BINOMIAL_MEAN() computes the Negative Binomial mean; NEGATIVE_BINOMIAL_SAMPLE() samples the Negative Binomial distribution; NEGATIVE_BINOMIAL_VARIANCE() computes the Negative Binomial variance. PDF parameter A = 2 PDF parameter B = 0.75 PDF mean = 2.66667 PDF variance = 0.888889 Sample size = 1000 Sample mean = 2.701000 Sample variance = 0.946546 Sample maximum = 11 Sample minimum = 2 NORMAL_01_CDF_TEST(): NORMAL_01_CDF() evaluates the Normal 01 CDF; NORMAL_01_CDF_INV() inverts the Normal 01 CDF. NORMAL_01_PDF() evaluates the Normal 01 PDF; X PDF CDF CDF_INV -0.944367 0.255418 0.172491 -0.944367 1.48881 0.131702 0.931731 1.48881 0.174626 0.392906 0.569313 0.174626 1.3186 0.167245 0.906349 1.3186 0.98221 0.246275 0.837002 0.98221 -0.623751 0.328417 0.266396 -0.623751 -1.06615 0.225988 0.143179 -1.06615 0.262035 0.385479 0.603353 0.262035 -1.04374 0.231394 0.148303 -1.04374 -1.1593 0.203737 0.123167 -1.1593 NORMAL_01_SAMPLE_TEST(): NORMAL_01_MEAN() computes the Normal 01 mean; NORMAL_01_SAMPLE() samples the Normal 01 PDF; NORMAL_01_VARIANCE() returns the Normal 01 variance. PDF mean = 0.000000 PDF variance = 1.000000 Sample size = 1000 Sample mean = 0.005801 Sample variance = 1.025008 Sample maximum = 3.606861 Sample minimum = -3.107253 NORMAL_CDF_TEST(): NORMAL_CDF() evaluates the Normal CDF; NORMAL_CDF_INV() inverts the Normal CDF. NORMAL_PDF() evaluates the Normal PDF; PDF parameter A = 100 PDF parameter B = 15 X PDF CDF CDF_INV 96.0829 0.0257046 0.396993 96.0829 91.0564 0.022265 0.275507 91.0564 75.7688 0.00721374 0.0531107 75.7688 121.429 0.0095861 0.923441 121.429 101.443 0.0264733 0.538324 101.443 75.1557 0.00674715 0.0488317 75.1557 104.297 0.0255267 0.612751 104.297 75.4687 0.00698292 0.0509805 75.4687 121.849 0.00920635 0.92739 121.849 91.7053 0.0228254 0.290139 91.7053 NORMAL_SAMPLE_TEST(): NORMAL_MEAN() computes the Normal mean; NORMAL_SAMPLES() samples the Normal distribution; NORMAL_VARIANCE() returns the Normal variance. PDF parameter MU = 100 PDF parameter SIGMA = 15 PDF mean = 100 PDF variance = 225 Sample size = 1000 Sample mean = 99.3963 Sample variance = 227.77 Sample maximum = 160.084 Sample minimum = 48.5434 NORMAL_TRUNCATED_AB_CDF_TEST(): NORMAL_TRUNCATED_AB_CDF() evaluates the Normal Truncated AB CDF. NORMAL_TRUNCATED_AB_CDF_INV() inverts the Normal Truncated AB CDF. NORMAL_TRUNCATED_AB_PDF() evaluates the Normal Truncated AB PDF. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] X PDF CDF CDF_INV 106.145 0.016221 0.601702 106.145 107.511 0.0159807 0.623701 107.511 99.9654 0.0167184 0.499422 99.9654 130.767 0.00783991 0.909406 130.767 115.763 0.0137044 0.747071 115.763 117.783 0.0129815 0.774022 117.783 60.1493 0.00469287 0.0342742 60.1493 124.347 0.010405 0.850909 124.347 109.005 0.0156682 0.647359 109.005 72.2435 0.00902653 0.11597 72.2435 NORMAL_TRUNCATED_AB_SAMPLE_TEST(): NORMAL_TRUNCATED_AB_MEAN() computes the Normal Truncated AB mean; NORMAL_TRUNCATED_AB_SAMPLE() samples the Normal Truncated AB distribution; NORMAL_TRUNCATED_AB_VARIANCE() computes the Normal Truncated AB variance. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,150] PDF mean = 100 PDF variance = 483.588 Sample size = 1000 Sample mean = 100.682 Sample variance = 507.346 Sample maximum = 149.986 Sample minimum = 50.1782 NORMAL_TRUNCATED_A_CDF_TEST(): NORMAL_TRUNCATED_A_CDF() evaluates the Normal Truncated A CDF. NORMAL_TRUNCATED_A_CDF_INV() inverts the Normal Truncated A CDF. NORMAL_TRUNCATED_A_PDF() evaluates the Normal Truncated A PDF. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo) X PDF CDF CDF_INV 78.5159 0.0112876 0.176332 78.5159 79.9946 0.0118554 0.193444 79.9946 118.392 0.0124579 0.763655 118.392 84.4286 0.01345 0.249618 84.4286 122.372 0.0109412 0.810262 122.372 92.0244 0.015519 0.3603 92.0244 133.487 0.00665825 0.907692 133.487 83.1772 0.0130208 0.233053 83.1772 78.6315 0.0113324 0.177638 78.6315 131.836 0.00725808 0.89621 131.836 NORMAL_TRUNCATED_A_SAMPLE_TEST(): NORMAL_TRUNCATED_A_MEAN() computes the Normal Truncated A mean; NORMAL_TRUNCATED_A_SAMPLE() samples the Normal Truncated A distribution; NORMAL_TRUNCATED_A_VARIANCE() computes the Normal Truncated A variance. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [50,+oo] PDF mean = 101.381 PDF variance = 554.032 Sample size = 1000 Sample mean = 101.451 Sample variance = 573.743 Sample maximum = 184.108 Sample minimum = 50.2562 NORMAL_TRUNCATED_B_CDF_TEST(): NORMAL_TRUNCATED_B_CDF() evaluates the Normal Truncated B CDF. NORMAL_TRUNCATED_B_CDF_INV() inverts the Normal Truncated B CDF. NORMAL_TRUNCATED_B_PDF() evaluates the Normal Truncated B PDF. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [-oo,150] X PDF CDF CDF_INV 86.4845 0.0141091 0.301238 86.4845 52.6793 0.00272252 0.02987 52.6793 107.715 0.0155698 0.635653 107.715 126.282 0.00939655 0.873306 126.282 118.787 0.0123124 0.791827 118.787 54.8243 0.00319081 0.0362024 54.8243 66.4779 0.0066457 0.0920738 66.4779 82.0697 0.012626 0.24213 82.0697 73.615 0.00935602 0.149011 73.615 88.593 0.0147149 0.331638 88.593 NORMAL_TRUNCATED_B_SAMPLE_TEST(): NORMAL_TRUNCATED_B_MEAN() computes the Normal Truncated B mean; NORMAL_TRUNCATED_B_SAMPLE() samples the Normal Truncated B distribution; NORMAL_TRUNCATED_B_VARIANCE() computes the Normal Truncated B variance. The "parent" normal distribution has mean = 100 standard deviation = 25 The parent distribution is truncated to the interval [-oo,150] PDF mean = 98.6188 PDF variance = 554.032 Sample size = 1000 Sample mean = 98.5983 Sample variance = 562.039 Sample maximum = 149.518 Sample minimum = 10.6528 pareto_cdf_test(): pareto_cdf() evaluates the Pareto CDF; pareto_cdf_inv() inverts the Pareto CDF. pareto_pdf() evaluates the Pareto PDF; PDF parameter A = 0.5 PDF parameter B = 5 X PDF CDF CDF_INV 0.614418 2.90426 0.643114 0.614418 0.527642 7.24079 0.235892 0.527642 0.629588 2.50889 0.684087 0.629588 0.554234 5.39087 0.402439 0.554234 0.591936 3.63223 0.569991 0.591936 0.504346 9.49398 0.0423495 0.504346 0.530578 7.00367 0.256801 0.530578 0.505885 9.32198 0.0568299 0.505885 0.502749 9.67637 0.0270426 0.502749 0.544325 6.00719 0.346028 0.544325 PARETO_SAMPLE_TEST(): PARETO_MEAN() computes the Pareto mean; PARETO_SAMPLE() samples the Pareto distribution; PARETO_VARIANCE() computes the Pareto variance. PDF parameter A = 0.5 PDF parameter B = 5 PDF mean = 0.625 PDF variance = 0.0260417 Sample size = 1000 Sample mean = 0.625599 Sample variance = 0.0214045 Sample maximum = 1.52063 Sample minimum = 0.500143 PEARSON_05_PDF_TEST(): PEARSON_05_PDF() evaluates the Pearson 05 PDF. PDF argument X = 5 PDF parameter A = 1 PDF parameter B = 2 PDF parameter C = 3 PDF value = 0.0758163 PLANCK_PDF_TEST(): PLANCK_PDF() evaluates the Planck PDF. PDF parameter A = 2 PDF parameter B = 3 X PDF 4.13702 0.0445054 1.08967 0.406589 2.15774 0.335168 1.86997 0.392033 0.787747 0.314209 1.99237 0.369253 1.35261 0.436836 1.48927 0.436156 0.550745 0.204908 1.65456 0.423348 PLANCK_SAMPLE_TEST(): PLANCK_MEAN() returns the mean of the Planck distribution. PLANCK_SAMPLE() samples the Planck distribution. PLANCK_VARIANCE() returns the variance of the Planck distribution. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 3.83223 PDF variance = 4.11319 Sample size = 1000 Sample mean = 1.87943 Sample variance = 1.00372 Sample maximum = 7.08154 Sample minimum = 0.0458139 POISSON_CDF_TEST(): POISSON_CDF() evaluates the Poisson CDF, POISSON_CDF_INV() inverts the Poisson CDF. POISSON_PDF() evaluates the Poisson PDF. PDF parameter A = 10 X PDF CDF CDF_INV 13 0.0729079 0.864464 13 8 0.112599 0.33282 8 15 0.0347181 0.95126 15 10 0.12511 0.58304 10 10 0.12511 0.58304 10 5 0.0378333 0.067086 5 14 0.0520771 0.916542 14 11 0.113736 0.696776 11 12 0.0947803 0.791556 12 3 0.00756665 0.0103361 3 POISSON_SAMPLE_TEST(): POISSON_MEAN() computes the Poisson mean; POISSON_SAMPLE() samples the Poisson distribution; POISSON_VARIANCE() computes the Poisson variance. PDF parameter A = 10 PDF mean = 10 PDF variance = 10 Sample size = 1000 Sample mean = 10.239000 Sample variance = 10.796676 Sample maximum = 25 Sample minimum = 2 POWER_CDF_TEST(): POWER_CDF() evaluates the Power CDF; POWER_CDF_INV() inverts the Power CDF. POWER_PDF() evaluates the Power PDF; PDF parameter A = 2 PDF parameter B = 3 X PDF CDF CDF_INV 2.17894 0.484209 0.527532 2.17894 2.18603 0.485785 0.53097 2.18603 2.81039 0.62453 0.877585 2.81039 1.23865 0.275254 0.170471 1.23865 0.749363 0.166525 0.0623938 0.749363 0.604688 0.134375 0.0406275 0.604688 2.70884 0.601964 0.81531 2.70884 1.56074 0.346832 0.270658 1.56074 0.695195 0.154488 0.0536996 0.695195 1.61776 0.359502 0.290793 1.61776 power_sample_test(): power_mean() computes the Power mean; power_sample() samples the Power distribution; power_variance() computes the Power variance. PDF parameter A = 2 PDF parameter B = 3 PDF mean = 2 PDF variance = 0.5 Sample size = 1000 Sample mean = 2.02937 Sample variance = 0.485037 Sample maximum = 2.99983 Sample minimum = 0.111553 quasigeometric_cdf_test(): quasigeometric_cdf() evaluates the Quasigeometric CDF; quasigeometric_cdf_inv() inverts the Quasigeometric CDF. quasigeometric_pdf() evaluates the Quasigeometric PDF; PDF parameter A = 0.4825 PDF parameter B = 0.5893 X PDF CDF CDF_INV 0 0.4825 0.4825 1 5 0.0256319 0.963222 6 0 0.4825 0.4825 1 0 0.4825 0.4825 1 1 0.212537 0.695037 2 2 0.125248 0.820285 3 0 0.4825 0.4825 1 1 0.212537 0.695037 2 0 0.4825 0.4825 1 1 0.212537 0.695037 2 quasigeometric_sample_test(): quasigeometric_mean() computes the Quasigeometric mean; quasigeometric_sample() samples the Quasigeometric distribution; quasigeometric_variance() computes the Quasigeometric variance. PDF parameter A = 0.4825 PDF parameter B = 0.5893 PDF parameter A = 0.4825 PDF mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.195000 Sample variance = 3.158133 Sample maximum = 11 Sample minimum = 0 r8_beta_test(): r8_beta() evaluates the Beta function. X Y BETA(X,Y) R8_BETA(X,Y) tabulated computed. 0.2 1 5 4.999999999999998 0.4 1 2.5 2.5 0.6 1 1.666666666666667 1.666666666666667 0.8 1 1.25 1.25 1 0.2 5 4.999999999999998 1 0.4 2.5 2.5 1 1 1 1 2 2 0.1666666666666667 0.1666666666666667 3 3 0.03333333333333333 0.03333333333333335 4 4 0.007142857142857143 0.00714285714285714 5 5 0.001587301587301587 0.001587301587301589 6 2 0.02380952380952381 0.0238095238095238 6 3 0.005952380952380952 0.005952380952380949 6 4 0.001984126984126984 0.001984126984126986 6 5 0.0007936507936507937 0.0007936507936507934 6 6 0.0003607503607503608 0.0003607503607503604 7 7 8.325008325008325e-05 8.325008325008314e-05 r8_gamma_inc_test(): r8_gamma_inc() evaluates the normalized incomplete Gamma function P(A,X). A X Exact F R8_GAMMA_INC(A,X) 0.1 0.03 0.738235 0.738235 0.1 0.3 0.908358 0.908358 0.1 1.5 0.988656 0.988656 0.5 0.075 0.301465 0.301465 0.5 0.75 0.779329 0.779329 0.5 3.5 0.991849 0.991849 1 0.1 0.0951626 0.0951626 1 1 0.632121 0.632121 1 5 0.993262 0.993262 1.1 0.1 0.0720597 0.0720597 1.1 1 0.589181 0.589181 1.1 5 0.991537 0.991537 2 0.15 0.0101858 0.0101858 2 1.5 0.442175 0.442175 2 7 0.992705 0.992705 6 2.5 0.042021 0.042021 6 12 0.979659 0.979659 11 16 0.922604 0.922604 26 25 0.447079 0.447079 41 45 0.744455 0.744455 r8_gamma_log_int_test(): r8_gamma_log_int() evaluates the logarithm of the gamma function for integer argument. I R8_GAMMA_LOG_INT(I) 1 0 2 0 3 0.693147 4 1.79176 5 3.17805 6 4.78749 7 6.57925 8 8.52516 9 10.6046 10 12.8018 11 15.1044 12 17.5023 13 19.9872 14 22.5522 15 25.1912 16 27.8993 17 30.6719 18 33.5051 19 36.3954 20 39.3399 r8_zeta_test(): r8_zeta() estimates the Zeta function. P R8_Zeta(P) 1 Inf 2 1.64493 3 1.20206 4 1.08232 5 1.03693 6 1.01734 7 1.00835 8 1.00408 9 1.00201 10 1.00099 11 1.00049 12 1.00025 13 1.00012 14 1.00006 15 1.00003 16 1.00002 17 1.00001 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 3 1.20206 3.125 1.17905 3.25 1.15915 3.375 1.14185 3.5 1.12673 3.625 1.11347 3.75 1.10179 3.875 1.09147 4 1.08232 RAYLEIGH_CDF_TEST(): RAYLEIGH_CDF() evaluates the Rayleigh CDF; RAYLEIGH_CDF_INV() inverts the Rayleigh CDF. RAYLEIGH_PDF() evaluates the Rayleigh PDF; PDF parameter A = 2 X PDF CDF CDF_INV 4.22556 0.113375 0.892677 4.22556 2.60594 0.27877 0.572101 2.60594 2.20901 0.300077 0.45663 2.20901 2.67316 0.273554 0.590667 2.67316 4.66875 0.0765314 0.934431 4.66875 1.36007 0.269825 0.206439 1.36007 2.39037 0.292562 0.510432 2.39037 1.3045 0.263635 0.191614 1.3045 3.20796 0.221566 0.723729 3.20796 2.37855 0.293173 0.506972 2.37855 RAYLEIGH_SAMPLE_TEST(): RAYLEIGH_MEAN() computes the Rayleigh mean; RAYLEIGH_SAMPLE() samples the Rayleigh distribution; RAYLEIGH_VARIANCE() computes the Rayleigh variance. PDF parameter A = 2 PDF mean = 2.50663 PDF variance = 1.71681 Sample size = 1000 Sample mean = 2.49667 Sample variance = 1.78806 Sample maximum = 7.78217 Sample minimum = 0.0709613 RECIPROCAL_CDF_TEST(): RECIPROCAL_CDF() evaluates the Reciprocal CDF. RECIPROCAL_CDF_INV() inverts the Reciprocal CDF. RECIPROCAL_PDF() evaluates the Reciprocal PDF. PDF parameter A = 1 PDF parameter B = 3 X PDF CDF CDF_INV 2.20703 0.412427 0.72059 2.20703 2.71766 0.334935 0.910031 2.71766 1.10635 0.822741 0.0919944 1.10635 2.99641 0.303777 0.998909 2.99641 2.1337 0.426601 0.689832 2.1337 1.19396 0.762371 0.161362 1.19396 2.40697 0.378169 0.799524 2.40697 1.3946 0.652686 0.302756 1.3946 2.13775 0.425792 0.69156 2.13775 1.46167 0.62274 0.345507 1.46167 RECIPROCAL_SAMPLE_TEST(): RECIPROCAL_MEAN() computes the Reciprocal mean; RECIPROCAL_SAMPLE() samples the Reciprocal distribution; RECIPROCAL_VARIANCE() computes the Reciprocal variance. PDF parameter A = 1 PDF parameter B = 3 PDF mean = 1.82048 PDF variance = 0.326815 Sample size = 1000 Sample mean = 1.82343 Sample variance = 0.335579 Sample maximum = 2.9991 Sample minimum = 1.00145 RUNS_PDF_TEST(): RUNS_PDF() evaluates the Runs PDF; M is the number of symbols of one kind, N is the number of symbols of the other kind, R is the number of runs (sequences of one symbol) M N R PDF 6 0 1 1 6 0 2 0 6 1.000000 6 1 1 0 6 1 2 0.285714 6 1 3 0.714286 6 1 4 0 6 1.000000 6 2 1 0 6 2 2 0.0714286 6 2 3 0.214286 6 2 4 0.357143 6 2 5 0.357143 6 2 6 0 6 1.000000 6 3 1 0 6 3 2 0.0238095 6 3 3 0.0833333 6 3 4 0.238095 6 3 5 0.297619 6 3 6 0.238095 6 3 7 0.119048 6 3 8 0 6 1.000000 6 4 1 0 6 4 2 0.00952381 6 4 3 0.0380952 6 4 4 0.142857 6 4 5 0.214286 6 4 6 0.285714 6 4 7 0.190476 6 4 8 0.0952381 6 4 9 0.0238095 6 4 10 0 6 1.000000 6 5 1 0 6 5 2 0.004329 6 5 3 0.0194805 6 5 4 0.0865801 6 5 5 0.151515 6 5 6 0.25974 6 5 7 0.21645 6 5 8 0.17316 6 5 9 0.0649351 6 5 10 0.021645 6 5 11 0.0021645 6 5 12 0 6 1.000000 6 6 1 0 6 6 2 0.0021645 6 6 3 0.0108225 6 6 4 0.0541126 6 6 5 0.108225 6 6 6 0.21645 6 6 7 0.21645 6 6 8 0.21645 6 6 9 0.108225 6 6 10 0.0541126 6 6 11 0.0108225 6 6 12 0.0021645 6 6 13 0 6 6 14 0 6 1.000000 6 7 1 0 6 7 2 0.0011655 6 7 3 0.00641026 6 7 4 0.034965 6 7 5 0.0786713 6 7 6 0.174825 6 7 7 0.203963 6 7 8 0.2331 6 7 9 0.145688 6 7 10 0.0874126 6 7 11 0.0262238 6 7 12 0.00699301 6 7 13 0.000582751 6 7 14 0 6 1.000000 6 8 1 0 6 8 2 0.000666001 6 8 3 0.003996 6 8 4 0.02331 6 8 5 0.0582751 6 8 6 0.13986 6 8 7 0.18648 6 8 8 0.2331 6 8 9 0.174825 6 8 10 0.11655 6 8 11 0.04662 6 8 12 0.013986 6 8 13 0.002331 6 8 14 0 6 1.000000 runs_sample_test(): runs_mean() computes the Runs mean; runs_sample() samples the Runs distribution. runs_variance() computes the Runs variance PDF parameter M = 10 PDF parameter N = 5 PDF mean = 7.66667 PDF variance = 2.69841 Sample size = 1000 Sample mean = 7.638000 Sample variance = 2.667624 Sample maximum = 11 Sample minimum = 3 sech_cdf_test(): sech_cdf() evaluates the Sech CDF. sech_cdf_inv() inverts the Sech CDF. sech_pdf() evaluates the Sech PDF. PDF parameter A = 3 PDF parameter B = 2 X PDF CDF CDF_INV 4.46506 0.12429 0.714742 4.46506 -1.42617 0.0343998 0.0693469 -1.42617 3.27172 0.157697 0.543113 3.27172 -2.28255 0.0225715 0.0452956 -2.28255 1.85419 0.136187 0.326867 1.85419 3.03621 0.159129 0.505763 3.03621 4.36029 0.128314 0.701509 4.36029 4.28707 0.131066 0.692013 4.28707 3.85129 0.145751 0.631571 3.85129 -4.57915 0.0071918 0.0143885 -4.57915 SECH_SAMPLE_TEST(): SECH_MEAN() computes the Sech mean; SECH_SAMPLE() samples the Sech distribution; SECH_VARIANCE() computes the Sech variance. PDF parameter A = 3 PDF parameter B = 2 PDF mean = 3 PDF variance = 9.8696 Sample size = 1000 Sample mean = 2.97448 Sample variance = 9.41821 Sample maximum = 17.1761 Sample minimum = -10.5258 SEMICIRCULAR_CDF_TEST(): SEMICIRCULAR_CDF() evaluates the Semicircular CDF. SEMICIRCULAR_CDF_INV() inverts the Semicircular CDF. SEMICIRCULAR_PDF() evaluates the Semicircular PDF. PDF parameter A = 3 PDF parameter B = 2 X PDF CDF CDF_INV 3.04551 0.318227 0.514485 3.04541 3.73861 0.295808 0.729648 3.73828 2.08538 0.283075 0.21936 2.08545 1.43362 0.19792 0.0585833 1.43359 4.22338 0.251814 0.863542 4.22363 1.82726 0.257845 0.149364 1.82715 2.96609 0.318264 0.489206 2.96582 2.03024 0.278388 0.203879 2.03027 4.50128 0.21031 0.928123 4.50098 3.09175 0.317975 0.529195 3.0918 SEMICIRCULAR_SAMPLE_TEST(): SEMICIRCULAR_MEAN() computes the Semicircular mean; SEMICIRCULAR_SAMPLE() samples the Semicircular distribution; SEMICIRCULAR_VARIANCE() computes the Semicircular variance. PDF parameter A = 3.000000 PDF parameter B = 2.000000 PDF mean = 3.000000 PDF variance = 1.000000 Sample size = 1000 Sample mean = 3.061918 Sample variance = 0.983693 Sample maximum = 4.995040 Sample minimum = 1.071871 STUDENT_CDF_TEST(): STUDENT_CDF() evaluates the Student CDF. STUDENT_PDF() evaluates the Student PDF. PDF argument X = 2.447 PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF value = 0.14754 CDF value = 0.816049 STUDENT_SAMPLE_TEST(): STUDENT_MEAN() computes the Student mean; STUDENT_SAMPLE() samples the Student distribution; STUDENT_VARIANCE() computes the Student variance. PDF parameter A = 0.5 PDF parameter B = 2 PDF parameter C = 6 PDF mean = 0.5 PDF variance = 6 Sample size = 1000 Sample mean = 0.504947 Sample variance = 2.02595 Sample maximum = 12.9819 Sample minimum = -6.83084 student_noncentral_cdf_test(): student_noncentral_cdf() evaluates the Student Noncentral CDF; PDF argument X = 0.5 PDF parameter IDF = 10 PDF parameter B = 1 CDF value = 0.30528 tfn_test(): tfn() evaluates Owen's T function. H A T(H,A) Exact 1 0.5 0.0430647 0.0430647 1 1 0.0667419 0.0667419 1 2 0.0784682 0.0784682 1 3 0.0792995 0.0792995 0.5 0.5 0.0644886 0.0644886 0.5 1 0.106671 0.106671 0.5 2 0.141581 0.141581 0.5 3 0.151084 0.151084 0.25 0.5 0.0713466 0.0713466 0.25 1 0.120129 0.120129 0.25 2 0.166613 0.166613 0.25 3 0.18475 0.18475 0.125 0.5 0.0731727 0.0731727 0.125 1 0.123763 0.123763 0.125 2 0.173744 0.173744 0.125 3 0.195119 0.195119 0.0078125 0.5 0.0737894 0.0737894 0.0078125 1 0.124995 0.124995 0.0078125 2 0.176198 0.176198 0.0078125 3 0.198777 0.198777 0.0078125 10 0.234074 0.234089 0.0078125 100 0.233737 0.247946 TRIANGLE_CDF_TEST(): TRIANGLE_CDF() evaluates the Triangle CDF; TRIANGLE_CDF_INV() inverts the Triangle CDF. TRIANGLE_PDF() evaluates the Triangle PDF; PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 10 X PDF CDF CDF_INV 8.81616 0.0375823 0.977754 8.81616 7.45571 0.0807713 0.897247 7.45571 6.1577 0.121978 0.765662 6.1577 9.72753 0.00864987 0.998822 9.72753 6.09464 0.12398 0.757908 6.09464 3.60087 0.203147 0.350019 3.60087 1.79095 0.0878832 0.0347555 1.79095 5.61658 0.139156 0.695011 5.61658 4.85861 0.163219 0.580414 4.85861 2.76587 0.196208 0.173239 2.76587 TRIANGLE_SAMPLE_TEST(): TRIANGLE_MEAN() returns the Triangle mean; TRIANGLE_SAMPLE() samples the Triangle distribution; TRIANGLE_VARIANCE() returns the Triangle variance; PDF parameter A = 1 PDF parameter B = 3 PDF parameter C = 10 PDF parameter MEAN = 4.66667 PDF parameter VARIANCE = 3.72222 Sample size = 1000 Sample mean = 4.64229 Sample variance = 3.67126 Sample maximum = 9.84706 Sample minimum = 1.1833 TRIANGULAR_CDF_TEST(): TRIANGULAR_CDF() evaluates the Triangular CDF; TRIANGULAR_CDF_INV() inverts the Triangular CDF. TRIANGULAR_PDF() evaluates the Triangular PDF; PDF parameter A = 1 PDF parameter B = 10 X PDF CDF CDF_INV 3.90038 0.143229 0.207708 3.90038 8.48047 0.0750385 0.942988 8.48047 2.45352 0.0717788 0.052166 2.45352 5.39232 0.216905 0.476357 5.39232 5.91998 0.201482 0.588974 5.91998 7.61107 0.117972 0.859087 7.61107 2.82693 0.0902189 0.082412 2.82693 7.69854 0.113652 0.869217 7.69854 2.10276 0.0544571 0.0300264 2.10276 4.03265 0.149761 0.227086 4.03265 TRIANGULAR_SAMPLE_TEST(): TRIANGULAR_MEAN() computes the Triangular mean; TRIANGULAR_SAMPLE() samples the Triangular distribution; TRIANGULAR_VARIANCE() computes the Triangular variance. PDF parameter A = 1 PDF parameter B = 10 PDF mean = 5.5 PDF variance = 3.375 Sample size = 1000 Sample mean = 5.52837 Sample variance = 3.2142 Sample maximum = 9.89622 Sample minimum = 1.12371 trigamma_test(): trigamma() evaluates the TriGamma function. X FX FX Tabulated Computed 1 1.644934066848226 1.644934065473016 1.1 1.433299150792759 1.43329914968199 1.2 1.267377205423779 1.267377204522996 1.3 1.134253434996619 1.134253434263296 1.4 1.025356590529597 1.025356589930374 1.5 0.9348022005446793 0.9348022000532704 1.6 0.8584318931245799 0.8584318927201864 1.7 0.7932328301639984 0.793232829830095 1.8 0.7369741375017002 0.7369741372251055 1.9 0.6879720582426356 0.6879720580127948 2 0.6449340668482264 0.6449340654730159 UNIFORM_01_ORDER_SAMPLE_TEST(): UNIFORM_ORDER_SAMPLE() samples the Uniform 01 Order distribution. Ordered sample: 1 0.0512269 2 0.0951427 3 0.254005 4 0.30607 5 0.340663 6 0.354029 7 0.632031 8 0.669324 9 0.724022 10 0.74594 UNIFORM_NSPHERE_SAMPLE_TEST(): UNIFORM_NSPHERE_SAMPLE() samples the Uniform Nsphere distribution. Dimension N of sphere = 3 Points on the sphere: 1 -0.528782 -0.437672 -0.727209 2 0.056396 0.807616 -0.587006 3 0.0437184 -0.961695 0.270613 4 -0.300021 -0.92382 -0.237789 5 0.742346 0.597742 0.3027 6 -0.263559 0.248654 -0.932045 7 0.672023 -0.734292 -0.0959198 8 -0.536597 -0.0881179 0.839225 9 -0.722903 0.663171 0.193949 10 -0.664306 0.352472 0.659137 uniform_01_cdf_test(): uniform_01_cdf() evaluates the Uniform 01 CDF; uniform_01_cdf_inv() inverts the Uniform 01 CDF. uniform_01_pdf() evaluates the Uniform 01 PDF; X PDF CDF CDF_INV 0.0970403 1 0.0970403 0.0970403 0.286074 1 0.286074 0.286074 0.937568 1 0.937568 0.937568 0.811458 1 0.811458 0.811458 0.253787 1 0.253787 0.253787 0.341393 1 0.341393 0.341393 0.662051 1 0.662051 0.662051 0.332143 1 0.332143 0.332143 0.739459 1 0.739459 0.739459 0.270922 1 0.270922 0.270922 UNIFORM_01_SAMPLE_TEST(): UNIFORM_01_MEAN() computes the Uniform 01 mean; UNIFORM_01_SAMPLE() samples the Uniform 01 distribution; UNIFORM_01_VARIANCE() computes the Uniform 01 variance. PDF mean = 0.5 PDF variance = 0.0833333 Sample size = 1000 Sample mean = 0.507889 Sample variance = 0.080764 Sample maximum = 0.998608 Sample minimum = 0.00168598 uniform_cdf_test(): uniform_cdf() evaluates the Uniform CDF; uniform_cdf_inv() inverts the Uniform CDF. uniform_pdf() evaluates the Uniform PDF; PDF parameter A = 1 PDF parameter B = 10 X PDF CDF CDF_INV 1.19025 0.111111 0.0211393 1.19025 7.75732 0.111111 0.750813 7.75732 1.29499 0.111111 0.0327766 1.29499 5.28218 0.111111 0.475798 5.28218 3.57756 0.111111 0.286396 3.57756 8.20824 0.111111 0.800916 8.20824 6.30921 0.111111 0.589913 6.30921 6.71345 0.111111 0.634828 6.71345 7.46157 0.111111 0.717952 7.46157 4.05974 0.111111 0.339972 4.05974 UNIFORM_SAMPLE_TEST(): UNIFORM_MEAN() computes the Uniform mean; UNIFORM_SAMPLE() samples the Uniform distribution; UNIFORM_VARIANCE() computes the Uniform variance. PDF parameter A = 1 PDF parameter B = 10 PDF mean = 5.5 PDF variance = 6.75 Sample size = 1000 Sample mean = 5.40345 Sample variance = 6.41775 Sample maximum = 9.98583 Sample minimum = 1.00512 UNIFORM_DISCRETE_CDF_TEST(): UNIFORM_DISCRETE_CDF() evaluates the Uniform Discrete CDF; UNIFORM_DISCRETE_CDF_INV() inverts the Uniform Discrete CDF. UNIFORM_DISCRETE_PDF() evaluates the Uniform Discrete PDF; PDF parameter A = 1 PDF parameter B = 6 X PDF CDF CDF_INV 2 0.166667 0.333333 3 6 0.166667 1 6 3 0.166667 0.5 4 1 0.166667 0.166667 2 4 0.166667 0.666667 5 2 0.166667 0.333333 3 4 0.166667 0.666667 5 3 0.166667 0.5 4 6 0.166667 1 6 5 0.166667 0.833333 6 UNIFORM_DISCRETE_SAMPLE_TEST(): UNIFORM_DISCRETE_MEAN() computes the Uniform Discrete mean; UNIFORM_DISCRETE_SAMPLE() samples the Uniform Discrete distribution; UNIFORM_DISCRETE_VARIANCE() computes the Uniform Discrete variance. PDF parameter A = 1 PDF parameter B = 6 PDF mean = 3.5 PDF variance = 2.91667 Sample size = 1000 Sample mean = 4.011000 Sample variance = 2.781661 Sample maximum = 6 Sample minimum = 1 von_mises_cdf_test(): von_mises_cdf() evaluates the Von Mises CDF. von_mises_cdf_inv() inverts the Von Mises CDF. von_mises_pdf() evaluates the Von Mises PDF. PDF parameter A = 1 PDF parameter B = 2 X PDF CDF CDF_INV -0.0196923 0.198967 0.106438 -0.0200972 2.40178 0.0977397 0.948443 2.40206 0.538464 0.418478 0.277625 0.538272 1.12599 0.507772 0.564655 1.12617 0.627253 0.449684 0.316196 0.627243 0.621008 0.447627 0.313394 0.621107 1.87377 0.252084 0.860738 1.8736 0.00804572 0.208512 0.112089 0.00828142 0.65404 0.458236 0.328357 0.654087 -1.05407 0.0275646 0.0157451 -1.05553 von_mises_sample_test(): von_mises_mean() computes the Von Mises mean; von_mises_sample() samples the Von Mises distribution. von_mises_circular_variance() computes the Von Mises circular variance; PDF parameter A = 1 PDF parameter B = 2 PDF mean = 1 PDF circular variance = 0.302225 Sample size = 1000 Sample mean = 1.02095 Sample circular variance = 0.305937 Sample maximum = 3.93785 Sample minimum = -2.14047 weibull_cdf_test(): weibull_cdf() evaluates the Weibull CDF; weibull_cdf_inv() inverts the Weibull CDF. weibull_pdf() evaluates the Weibull PDF; PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 X PDF CDF CDF_INV 5.90802 0.165508 0.943847 5.90802 5.38873 0.377259 0.803685 5.38873 4.95938 0.496513 0.612071 4.95938 5.23449 0.432662 0.741085 5.23449 5.79682 0.207777 0.923129 5.79682 4.15348 0.37817 0.233182 4.15348 5.68212 0.254852 0.896624 5.68212 5.06716 0.477831 0.664657 5.06716 4.84922 0.506296 0.556749 4.84922 3.76233 0.239949 0.11227 3.76233 weibull_sample_test(): weibull_mean() computes the Weibull mean; weibull_sample() samples the Weibull distribution; weibull_variance() computes the Weibull variance. PDF parameter A = 2 PDF parameter B = 3 PDF parameter C = 4 PDF mean = 4.71921 PDF variance = 0.581953 Sample size = 1000 Sample mean = 4.70331 Sample variance = 0.607566 Sample maximum = 7.02372 Sample minimum = 2.61432 weibull_discrete_cdf_test(): weibull_discrete_cdf() evaluates the Weibull Discrete CDF; weibull_discrete_cdf_inv() inverts the Weibull Discrete CDF. weibull_discrete_pdf() evaluates the Weibull Discrete PDF; PDF parameter A = 0.5 PDF parameter B = 1.5 X PDF CDF CDF_INV 0 0.5 0.5 1 0 0.5 0.5 1 2 0.113508 0.972723 3 0 0.5 0.5 1 1 0.359214 0.859214 1 0 0.5 0.5 1 1 0.359214 0.859214 1 1 0.359214 0.859214 1 0 0.5 0.5 1 0 0.5 0.5 1 weibull_discrete_sample_test(): weibull_discrete_sample() samples the Weibull Discrete distribution PDF parameter A = 0.5 PDF parameter B = 1.5 Sample size = 1000 Sample mean = 0.691000 Sample variance = 0.636155 Sample maximum = 4 Sample minimum = 0 zipf_cdf_test(): zipf_pdf() evaluates the Zipf PDF. zipf_cdf() evaluates the Zipf CDF. zipf_cdf_inv() inverts the Zipf CDF. PDF parameter A = 2.000000 X PDF(X) CDF(X) CDF_INV(CDF) 1 0.607927 0.607927 1 2 0.151982 0.759909 2 3 0.0675475 0.827456 3 4 0.0379954 0.865452 4 5 0.0243171 0.889769 5 6 0.0168869 0.906656 6 7 0.0124067 0.919062 7 8 0.00949886 0.928561 8 9 0.00750527 0.936067 9 10 0.00607927 0.942146 10 11 0.00502419 0.94717 11 12 0.00422172 0.951392 12 13 0.0035972 0.954989 13 14 0.00310167 0.958091 14 15 0.0027019 0.960792 15 16 0.00237472 0.963167 16 17 0.00210355 0.965271 17 18 0.00187632 0.967147 18 19 0.00168401 0.968831 19 20 0.00151982 0.970351 20 zipf_sample_test(): zipf_mean() returns the mean of the Zipf distribution. zipf_sample() samples the Zipf distribution. zipf_variance() returns the variance of the Zipf distribution. PDF parameter A = 4.000000 PDF mean = 1.110627 PDF variance = 0.286326 Sample size = 1000 Sample mean = 1.128000 Sample variance = 0.269886 Sample maximum = 7 Sample minimum = 1 prob_test(): Normal end of execution. 11-Nov-2022 18:44:20