6 October 2025 6:33:06.972 PM prob_test(): Fortran90 version: Test prob(). angle_cdf_test(): angle_cdf() evaluates the Angle CDF; PDF parameter N = 5 PDF argument X = 0.500000 CDF value = 0.107809E-01 ANGLE_MEAN_test(): ANGLE_mean() computes the Angle mean; PDF parameter N = 5 PDF mean = 1.57080 ANGLE_PDF_test(): ANGLE_PDF evaluates the Angle PDF; PDF parameter N = 5 PDF argument X = 0.500000 PDF value = 0.826466E-01 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 -0.519335 -0.250573 0.691347E-01 -0.519335 -0.251946 0.277804 0.258582 -0.251946 -0.273411E-01 0.667403 0.472673 -0.273411E-01 0.558574 0.945474 0.949427 0.558574 0.659021E-01 0.793904 0.565711 0.659021E-01 0.271341 0.970689 0.758218 0.271341 -0.543937 -0.297884 0.571792E-01 -0.543937 -0.499815 -0.212598 0.793643E-01 -0.499815 0.127951E-01 0.724968 0.512794 0.127951E-01 0.427479 0.997582 0.877271 0.427479 ANGLIT_SAMPLE_test(): ANGLIT_mean() computes the Anglit mean; ANGLIT_sample() samples the Anglit distribution; ANGLIT_variance() computes the Anglit variance. PDF mean = 0.00000 PDF variance = 0.116850 Sample size = 1000 Sample mean = -0.133732E-02 Sample variance = 0.121516 Sample maximum = 0.725395 Sample minimum = -0.775272 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 = 1.00000 X PDF CDF CDF_INV 0.841885 0.589837 0.818554 0.841885 -0.377403E-01 0.318537 0.487984 -0.377403E-01 -0.664013 0.425707 0.268852 -0.664013 0.677452 0.432741 0.736916 0.677452 -0.997990 5.02242 0.201873E-01 -0.997990 0.491089 0.365407 0.663401 0.491089 -0.394208 0.346357 0.371019 -0.394208 0.642054 0.415191 0.721917 0.642054 0.738910 0.472407 0.764659 0.738910 0.982034 1.68681 0.939571 0.982034 ARCSIN_SAMPLE_test(): ARCSIN_mean() computes the Arcsin mean; ARCSIN_sample() samples the Arcsin distribution; ARCSIN_variance() computes the Arcsin variance. PDF parameter A = 1.00000 PDF mean = 0.00000 PDF variance = 0.500000 Sample size = 1000 Sample mean = 0.175344E-01 Sample variance = 0.522660 Sample maximum = 0.999995 Sample minimum = -0.999996 PDF parameter A = 16.0000 PDF mean = 0.00000 PDF variance = 128.000 Sample size = 1000 Sample mean = -0.216543E-01 Sample variance = 131.264 Sample maximum = 16.0000 Sample minimum = -16.0000 benford_cdf_test(): benford_cdf() evaluates the CDF. benford_cdf_invert() inverts the CDF. benford_pdf() evaluates the PDF. N CDF(N) CDF(N) by summing 1 0.301030 0.301030 2 0.477121 0.477121 3 0.602060 0.602060 4 0.698970 0.698970 5 0.778151 0.778151 6 0.845098 0.845098 7 0.903090 0.903090 8 0.954243 0.954243 9 1.00000 1.00000 N CDF(N) CDF(N) by summing 10 0.413927E-01 0.413927E-01 11 0.791812E-01 0.791812E-01 12 0.113943 0.113943 13 0.146128 0.146128 14 0.176091 0.176091 15 0.204120 0.204120 16 0.230449 0.230449 17 0.255273 0.255273 18 0.278754 0.278754 19 0.301030 0.301030 20 0.322219 0.322219 21 0.342423 0.342423 22 0.361728 0.361728 23 0.380211 0.380211 24 0.397940 0.397940 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 0.505150 0.505150 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 0.602060 0.602060 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 0.698970 0.698970 50 0.707570 0.707570 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 0.785330 0.785330 61 0.792392 0.792392 62 0.799341 0.799341 63 0.806180 0.806180 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 0.903090 0.903090 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 0.949390 0.949390 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 1.00000 1.00000 X PDF CDF CDF_INV 7 0.579919E-01 0.903090 7 7 0.579919E-01 0.903090 7 1 0.301030 0.301030 1 3 0.124939 0.602060 3 7 0.579919E-01 0.903090 7 4 0.969100E-01 0.698970 4 3 0.124939 0.602060 3 2 0.176091 0.477121 2 2 0.176091 0.477121 2 3 0.124939 0.602060 3 benford_pdf_test(): benford_pdf() evaluates the PDF. N PDF(N) 1 0.301030 2 0.176091 3 0.124939 4 0.969100E-01 5 0.791812E-01 6 0.669468E-01 7 0.579919E-01 8 0.511525E-01 9 0.457575E-01 N PDF(N) 10 0.413927E-01 11 0.377886E-01 12 0.347621E-01 13 0.321847E-01 14 0.299632E-01 15 0.280287E-01 16 0.263289E-01 17 0.248236E-01 18 0.234811E-01 19 0.222764E-01 20 0.211893E-01 21 0.202034E-01 22 0.193052E-01 23 0.184834E-01 24 0.177288E-01 25 0.170333E-01 26 0.163904E-01 27 0.157943E-01 28 0.152400E-01 29 0.147233E-01 30 0.142404E-01 31 0.137883E-01 32 0.133640E-01 33 0.129650E-01 34 0.125891E-01 35 0.122345E-01 36 0.118992E-01 37 0.115819E-01 38 0.112810E-01 39 0.109954E-01 40 0.107239E-01 41 0.104654E-01 42 0.102192E-01 43 0.998422E-02 44 0.975984E-02 45 0.954532E-02 46 0.934003E-02 47 0.914338E-02 48 0.895484E-02 49 0.877392E-02 50 0.860017E-02 51 0.843317E-02 52 0.827253E-02 53 0.811789E-02 54 0.796893E-02 55 0.782534E-02 56 0.768683E-02 57 0.755314E-02 58 0.742402E-02 59 0.729924E-02 60 0.717858E-02 61 0.706185E-02 62 0.694886E-02 63 0.683942E-02 64 0.673338E-02 65 0.663058E-02 66 0.653087E-02 67 0.643411E-02 68 0.634018E-02 69 0.624895E-02 70 0.616031E-02 71 0.607415E-02 72 0.599036E-02 73 0.590886E-02 74 0.582954E-02 75 0.575233E-02 76 0.567713E-02 77 0.560388E-02 78 0.553249E-02 79 0.546290E-02 80 0.539503E-02 81 0.532883E-02 82 0.526424E-02 83 0.520119E-02 84 0.513964E-02 85 0.507953E-02 86 0.502080E-02 87 0.496342E-02 88 0.490733E-02 89 0.485250E-02 90 0.479888E-02 91 0.474644E-02 92 0.469512E-02 93 0.464491E-02 94 0.459575E-02 95 0.454763E-02 96 0.450050E-02 97 0.445434E-02 98 0.440912E-02 99 0.436481E-02 benford_sample_test(): benford_mean() computes the mean; benford_sample() samples the distribution; benford_variance() computes the variance. PDF mean = 3.44024 PDF variance = 6.05651 Sample size = 1000 Sample mean = 3.40600 Sample variance = 5.81298 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 1.00000 1 1 0.750000 1.00000 1 0 0.250000 0.250000 0 1 0.750000 1.00000 1 1 0.750000 1.00000 1 1 0.750000 1.00000 1 1 0.750000 1.00000 1 1 0.750000 1.00000 1 1 0.750000 1.00000 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 = 0.755000 Sample variance = 0.185160 Sample maximum = 1 Sample minimum = 0 BESSEL_I0_TEST: BESSEL_I0 evaluates the Bessel I0 function. X Exact BESSEL_I0(X) 0.000000 1.000000000000000 1.000000000000000 0.200000 1.010025027795146 1.010025027795146 0.400000 1.040401782229341 1.040401782229341 0.600000 1.092045364317340 1.092045364317339 0.800000 1.166514922869803 1.166514922869803 1.000000 1.266065877752008 1.266065877752008 1.200000 1.393725584134064 1.393725584134064 1.400000 1.553395099731217 1.553395099731216 1.600000 1.749980639738909 1.749980639738909 1.800000 1.989559356618051 1.989559356618051 2.000000 2.279585302336067 2.279585302336067 2.500000 3.289839144050123 3.289839144050123 3.000000 4.880792585865024 4.880792585865024 3.500000 7.378203432225480 7.378203432225480 4.000000 11.30192195213633 11.30192195213633 4.500000 17.48117185560928 17.48117185560928 5.000000 27.23987182360445 27.23987182360445 6.000000 67.23440697647798 67.23440697647796 8.000000 427.5641157218048 427.5641157218047 10.000000 2815.716628466254 2815.716628466254 BESSEL_I1_TEST: BESSEL_I1 evaluates the Bessel I1 function. X Exact BESSEL_I1(X) 0.000000 0.000000000000000 0.000000000000000 0.200000 0.1005008340281251 0.1005008340281251 0.400000 0.2040267557335706 0.2040267557335706 0.600000 0.3137040256049221 0.3137040256049221 0.800000 0.4328648026206398 0.4328648026206398 1.000000 0.5651591039924850 0.5651591039924849 1.200000 0.7146779415526431 0.7146779415526432 1.400000 0.8860919814143274 0.8860919814143273 1.600000 1.084810635129880 1.084810635129880 1.800000 1.317167230391899 1.317167230391899 2.000000 1.590636854637329 1.590636854637329 2.500000 2.516716245288698 2.516716245288698 3.000000 3.953370217402609 3.953370217402608 3.500000 6.205834922258365 6.205834922258364 4.000000 9.759465153704451 9.759465153704447 4.500000 15.38922275373592 15.38922275373592 5.000000 24.33564214245053 24.33564214245052 6.000000 61.34193677764024 61.34193677764024 8.000000 399.8731367825601 399.8731367825602 10.000000 2670.988303701255 2670.988303701254 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 = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4 X PDF CDF CDF_INV 0 0.214286 0.214286 0 0 0.214286 0.214286 0 1 0.285714 0.500000 1 0 0.214286 0.214286 0 3 0.171429 0.928571 3 1 0.285714 0.500000 1 1 0.285714 0.500000 1 3 0.171429 0.928571 3 1 0.285714 0.500000 1 2 0.257143 0.757143 2 BETA_BINOMIAL_SAMPLE_test(): BETA_BINOMIAL_mean() computes the Beta Binomial mean; BETA_BINOMIAL_sample() samples the Beta Binomial distribution; BETA_BINOMIAL_variance() computes the Beta Binomial variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4 PDF mean = 1.60000 PDF variance = 1.44000 Sample size = 1000 Sample mean = 1.60400 Sample variance = 1.45864 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 = 12.0000 PDF parameter B = 12.0000 A B X PDF CDF CDF_INV 12.0000 12.0000 0.592085 2.64651 0.816111 0.592085 12.0000 12.0000 0.447344 3.42172 0.304323 0.447344 12.0000 12.0000 0.613510 2.16142 0.867638 0.613510 12.0000 12.0000 0.542263 3.57494 0.659294 0.542263 12.0000 12.0000 0.412297 2.74303 0.195698 0.412297 12.0000 12.0000 0.615357 2.11943 0.871590 0.615357 12.0000 12.0000 0.339104 1.16227 0.544559E-01 0.339104 12.0000 12.0000 0.604479 2.36723 0.847187 0.604479 12.0000 12.0000 0.487436 3.84154 0.451509 0.487436 12.0000 12.0000 0.586619 2.76667 0.801314 0.586619 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) 0.5000 0.5000 0.0100 0.637686E-01 0.637686E-01 0.5000 0.5000 0.1000 0.204833 0.204833 0.5000 0.5000 1.0000 1.00000 1.00000 1.0000 0.5000 0.0000 0.00000 0.00000 1.0000 0.5000 0.0100 0.501256E-02 0.501256E-02 1.0000 0.5000 0.1000 0.513167E-01 0.513167E-01 1.0000 0.5000 0.5000 0.292893 0.292893 1.0000 1.0000 0.5000 0.500000 0.500000 2.0000 2.0000 0.1000 0.280000E-01 0.280000E-01 2.0000 2.0000 0.2000 0.104000 0.104000 2.0000 2.0000 0.3000 0.216000 0.216000 2.0000 2.0000 0.4000 0.352000 0.352000 2.0000 2.0000 0.5000 0.500000 0.500000 2.0000 2.0000 0.6000 0.648000 0.648000 2.0000 2.0000 0.7000 0.784000 0.784000 2.0000 2.0000 0.8000 0.896000 0.896000 2.0000 2.0000 0.9000 0.972000 0.972000 5.5000 5.0000 0.5000 0.436191 0.436191 10.0000 0.5000 0.9000 0.151641 0.151641 10.0000 5.0000 0.5000 0.897827E-01 0.897827E-01 10.0000 5.0000 1.0000 1.00000 1.00000 10.0000 10.0000 0.5000 0.500000 0.500000 20.0000 5.0000 0.8000 0.459877 0.459877 20.0000 10.0000 0.6000 0.214682 0.214682 20.0000 10.0000 0.8000 0.950736 0.950736 20.0000 20.0000 0.5000 0.500000 0.500000 20.0000 20.0000 0.6000 0.897941 0.897941 30.0000 10.0000 0.7000 0.224130 0.224130 30.0000 10.0000 0.8000 0.758641 0.758641 40.0000 20.0000 0.7000 0.700178 0.700178 1.0000 0.5000 0.1000 0.513167E-01 0.513167E-01 1.0000 0.5000 0.2000 0.105573 0.105573 1.0000 0.5000 0.3000 0.163340 0.163340 1.0000 0.5000 0.4000 0.225403 0.225403 1.0000 2.0000 0.2000 0.360000 0.360000 1.0000 3.0000 0.2000 0.488000 0.488000 1.0000 4.0000 0.2000 0.590400 0.590400 1.0000 5.0000 0.2000 0.672320 0.672320 2.0000 2.0000 0.3000 0.216000 0.216000 3.0000 2.0000 0.3000 0.837000E-01 0.837000E-01 4.0000 2.0000 0.3000 0.307800E-01 0.307800E-01 5.0000 2.0000 0.3000 0.109350E-01 0.109350E-01 1.3062 11.7562 0.2256 0.918885 0.918885 1.3062 11.7562 0.0336 0.210530 0.210530 1.3062 11.7562 0.0295 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 = 2.00000 PDF parameter B = 3.00000 PDF mean = 0.400000 PDF variance = 0.400000E-01 Sample size = 1000 Sample mean = 0.409965 Sample variance = 0.410212E-01 Sample maximum = 0.951280 Sample minimum = 0.106797E-01 BINOMIAL_CDF_test(): BINOMIAL_CDF evaluates the Binomial CDF; BINOMIAL_CDF_INV inverts the Binomial CDF. BINOMIAL_PDF evaluates the Binomial PDF; PDF parameter A = 5 PDF parameter B = 0.650000 X PDF CDF CDF_INV 3 0.336416 0.571585 3 2 0.181147 0.235169 2 4 0.312386 0.883971 4 4 0.312386 0.883971 4 4 0.312386 0.883971 4 2 0.181147 0.235169 2 4 0.312386 0.883971 4 3 0.336416 0.571585 3 4 0.312386 0.883971 4 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 = 1.50000 PDF variance = 1.05000 Sample size = 1000 Sample mean = 1.46500 Sample variance = 1.06584 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 0.00000 0.00000 1 2 0.273973E-02 0.273973E-02 2 3 0.546444E-02 0.820417E-02 3 4 0.815175E-02 0.163559E-01 4 5 0.107797E-01 0.271356E-01 5 6 0.133269E-01 0.404625E-01 6 7 0.157732E-01 0.562357E-01 7 8 0.180996E-01 0.743353E-01 8 9 0.202885E-01 0.946238E-01 9 10 0.223243E-01 0.116948 10 11 0.241932E-01 0.141141 11 12 0.258834E-01 0.167025 12 13 0.273855E-01 0.194410 13 14 0.286922E-01 0.223103 14 15 0.297988E-01 0.252901 15 16 0.307027E-01 0.283604 16 17 0.314037E-01 0.315008 17 18 0.319038E-01 0.346911 18 19 0.322071E-01 0.379119 19 20 0.323199E-01 0.411438 20 21 0.322500E-01 0.443688 21 22 0.320070E-01 0.475695 22 23 0.316019E-01 0.507297 23 24 0.310470E-01 0.538344 24 25 0.303554E-01 0.568700 25 26 0.295411E-01 0.598241 26 27 0.286185E-01 0.626859 27 28 0.276022E-01 0.654461 28 29 0.265071E-01 0.680969 29 30 0.253477E-01 0.706316 30 BIRTHDAY_SAMPLE_test(): BIRTHDAY_sample() samples the Birthday distribution. N Mean PDF 10 0.247000E-01 0.223243E-01 11 0.257000E-01 0.241932E-01 12 0.261000E-01 0.258834E-01 13 0.240000E-01 0.273855E-01 14 0.300000E-01 0.286922E-01 15 0.327000E-01 0.297988E-01 16 0.325000E-01 0.307027E-01 17 0.343000E-01 0.314037E-01 18 0.330000E-01 0.319038E-01 19 0.312000E-01 0.322071E-01 20 0.324000E-01 0.323199E-01 21 0.331000E-01 0.322500E-01 22 0.318000E-01 0.320070E-01 23 0.293000E-01 0.316019E-01 24 0.287000E-01 0.310470E-01 25 0.304000E-01 0.303554E-01 26 0.313000E-01 0.295411E-01 27 0.270000E-01 0.286185E-01 28 0.285000E-01 0.276022E-01 29 0.255000E-01 0.265071E-01 30 0.263000E-01 0.253477E-01 31 0.267000E-01 0.241384E-01 32 0.229000E-01 0.228929E-01 33 0.197000E-01 0.216243E-01 34 0.225000E-01 0.203450E-01 35 0.194000E-01 0.190664E-01 36 0.180000E-01 0.177989E-01 37 0.181000E-01 0.165519E-01 38 0.128000E-01 0.153338E-01 39 0.118000E-01 0.141518E-01 40 0.143000E-01 0.130121E-01 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 1.45784 0.911745 0.623513 1.45784 1.30325 1.13316 0.466690 1.30325 1.50907 0.856295 0.668774 1.50907 1.30176 1.13581 0.465006 1.30176 1.16420 1.44985 0.288911 1.16420 1.60693 0.767175 0.748050 1.60693 1.72843 0.679386 0.835712 1.72843 1.05457 1.85959 0.109371 1.05457 1.06856 1.79486 0.134930 1.06856 1.07923 1.74846 0.153822 1.07923 BRADFORD_SAMPLE_test(): BRADFORD_mean() computes the Bradford mean; BRADFORD_sample() samples the Bradford distribution; BRADFORD_variance() computes Bradford the variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF mean = 1.38801 PDF variance = 0.807807E-01 Sample size = 1000 Sample mean = 1.38671 Sample variance = 0.838697E-01 Sample maximum = 1.99948 Sample minimum = 1.00013 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 9 3.333333 0.191741 100 90 3.333333 0.191741 10000 9536 3.145973 0.438050E-02 1000000 954388 3.143376 0.178300E-02 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 0.00000 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 4 5.000000 1.85841 100 62 3.225806 0.842138E-01 10000 6394 3.127932 0.136602E-01 1000000 636896 3.140230 0.136254E-02 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF parameter D = 2.00000 X PDF CDF CDF_INV 2.82080 0.460336 0.675169 2.82080 2.85099 0.445996 0.688846 2.85099 2.11785 0.578296 0.275202 2.11785 2.74274 0.496514 0.637810 2.74274 2.56305 0.568285 0.541815 2.56305 3.41624 0.207514 0.869041 3.41624 2.94912 0.399059 0.730309 2.94912 3.17650 0.296314 0.809111 3.17650 3.79065 0.113771 0.927606 3.79065 3.32787 0.237531 0.849399 3.32787 BURR_SAMPLE_test(): BURR_mean() computes the Burr mean; BURR_variance() computes the Burr variance; BURR_sample() samples the Burr distribution; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF parameter D = 2.00000 PDF mean = 2.61227 PDF variance = 0.625130 Sample size = 1000 Sample mean = 2.60900 Sample variance = 0.657541 Sample maximum = 8.60515 Sample minimum = 1.13530 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 = 0.00000 PDF parameter B = 0.250000 X PDF CDF CDF_INV 0.572549 0.226042 0.634237 0.572549 -0.415589 0.231959 0.401729 -0.415588 0.428832 0.231527 0.601340 0.428830 0.375582 0.233185 0.588966 0.375582 2.89022 0.820785E-01 0.979786 2.89021 2.75492 0.854527E-01 0.968469 2.75492 1.46888 0.167251 0.812944 1.46888 -0.879707 0.209876 0.298672 -0.879707 -0.626745 0.223608 0.353577 -0.626745 -1.66523 0.151652 0.155748 -1.66523 CARDIOID_SAMPLE_test(): CARDIOID_mean() computes the Cardioid mean; CARDIOID_sample() samples the Cardioid distribution; CARDIOID_variance() computes the Cardioid variance. PDF parameter A = 0.00000 PDF parameter B = 0.250000 PDF mean = 0.00000 PDF variance = 0.00000 Sample size = 1000 Sample mean = 0.109706E-01 Sample variance = 2.30872 Sample maximum = 3.13223 Sample minimum = -3.13383 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 = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 2.37506 0.104470 0.539590 2.37506 1.34248 0.101240 0.431321 1.34248 0.577818 0.866338E-01 0.359090 0.577818 2.10310 0.105978 0.510935 2.10310 0.965849 0.948342E-01 0.394334 0.965849 -2.73669 0.303767E-01 0.179713 -2.73669 0.904621 0.936219E-01 0.388564 0.904621 1.81529 0.105703 0.480426 1.81529 -6.30994 0.122341E-01 0.110279 -6.30994 8.96298 0.166123E-01 0.870507 8.96298 cauchy_sample_test(): cauchy_variance() computes the Cauchy variance; PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = Infinite PDF variance = Infinite Sample size = 1000 Sample mean = 2.94206 Sample variance = 3945.61 Sample maximum = 799.466 Sample minimum = -717.636 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 0.615989E-01 0.318916 0.519620 0.615989E-01 0.644738 0.416416 0.723034 0.644738 0.808990 0.541507 0.799985 0.808990 0.194606 0.324514 0.562343 0.194606 -0.611444 0.402268 0.290589 -0.611444 0.757946E-01 0.319228 0.524149 0.757946E-01 -0.644938 0.416508 0.276883 -0.644938 0.583083 0.391808 0.698154 0.583083 0.672342 0.430009 0.734711 0.672342 -0.997683 4.67828 0.216745E-01 -0.997683 CHEBYSHEV1_SAMPLE_test(): CHEBYSHEV1_mean() computes the Chebyshev1 mean; CHEBYSHEV1_sample() samples the Chebyshev1 distribution; CHEBYSHEV1_variance() computes the Chebyshev1 variance. PDF mean = 0.00000 PDF variance = 0.500000 Sample size = 1000 Sample mean = -0.914541E-02 Sample variance = 0.480316 Sample maximum = 0.999800 Sample minimum = -1.00000 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 3.71969 0.292648 0.395707 3.71973 3.11157 0.254689 0.226469 3.11133 5.79734 0.129262 0.875768 5.79688 4.05556 0.289858 0.493983 4.05566 2.69317 0.199812 0.130733 2.69336 3.69852 0.292270 0.389516 3.69824 5.64096 0.145482 0.854295 5.64062 5.64814 0.144720 0.855338 5.64844 2.36669 0.147499 0.739115E-01 2.36719 2.27530 0.132367 0.611232E-01 2.27539 CHI_SAMPLE_test(): CHI_mean() computes the Chi mean; CHI_variance() computes the Chi variance; CHI_sample() samples the Chi distribution. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF mean = 4.19154 PDF variance = 1.81408 Sample size = 1000 Sample mean = 4.16394 Sample variance = 1.66724 Sample maximum = 8.97387 Sample minimum = 1.18461 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 = 4.00000 X PDF CDF CDF_INV 3.57000 0.149759 0.532685 3.57000 7.93649 0.375130E-01 0.906067 7.93649 5.22852 0.957107E-01 0.735356 5.22852 5.33119 0.927068E-01 0.745028 5.33119 3.04206 0.166162 0.449189 3.04206 1.74846 0.182357 0.218103 1.74846 2.44315 0.180039 0.345157 2.44315 9.90331 0.175083E-01 0.957912 9.90331 2.99822 0.167397 0.441877 2.99822 4.76339 0.110027 0.687553 4.76339 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 = 10.0000 PDF mean = 10.0000 PDF variance = 20.0000 Sample size = 1000 Sample mean = 10.2144 Sample variance = 19.9606 Sample maximum = 31.9220 Sample minimum = 1.91143 CHI_SQUARE_NONCENTRAL_SAMPLE_test(): CHI_SQUARE_NONCENTRAL_mean() computes the Chi Square Noncentral mean. CHI_SQUARE_NONCENTRAL_sample() samples the Chi Square Noncentral distribution. CHI_SQUARE_NONCENTRAL_variance() computes the Chi Square Noncentral variance. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 5.00000 PDF variance = 14.0000 Sample size = 1000 Sample mean = 5.02151 Sample variance = 13.2519 Sample maximum = 25.2970 Sample minimum = 0.359848E-02 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 = 0.00000 0.00000 PDF variances = 1.00000 1.00000 Sample size = 1000 Sample mean = 0.826280E-02 -0.736967E-01 Sample variance = 1.02541 0.981566 Sample maximum = 3.19675 3.20579 Sample minimum = -3.63643 -3.05251 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 = 1.00000 5.00000 PDF variances = 0.562500 0.562500 Sample size = 1000 Sample mean = 0.997795 4.99589 Sample variance = 0.585764 0.549291 Sample maximum = 3.39277 7.25793 Sample minimum = -1.78435 2.64941 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 = 2.00000 PDF parameter B = 1.00000 X PDF CDF CDF_INV 3.20264 0.572791E-01 0.839897 3.20264 1.39638 0.131030 0.313590 1.39638 0.816534 0.601156E-01 0.164281 0.816534 2.90965 0.977246E-01 0.770395 2.90965 1.16628 0.106972 0.249466 1.16628 1.60155 0.146687 0.374834 1.60155 2.65194 0.126513 0.700324 2.65194 3.17043 0.620319E-01 0.832848 3.17043 -0.650719 -0.140362 0.309988E-02 -0.650719 2.24774 0.154296 0.578455 2.24774 COSINE_SAMPLE_test(): COSINE_mean() computes the Cosine mean; COSINE_sample() samples the Cosine distribution; COSINE_variance() computes the Cosine variance. PDF parameter A = 2.00000 PDF parameter B = 1.00000 PDF mean = 2.00000 PDF variance = 1.28987 Sample size = 1000 Sample mean = 2.03249 Sample variance = 1.35232 Sample maximum = 4.89616 Sample minimum = -0.896156 coupon_complete_pdf_test(): coupon_complete_pdf() evaluates the coupon collector's complete collection PDF. Number of coupon types is 2 BOX_NUM PDF CDF 1 0.00000 0.00000 2 0.500000 0.500000 3 0.250000 0.750000 4 0.125000 0.875000 5 0.625000E-01 0.937500 6 0.312500E-01 0.968750 7 0.156250E-01 0.984375 8 0.781250E-02 0.992188 9 0.390625E-02 0.996094 10 0.195312E-02 0.998047 11 0.976562E-03 0.999023 12 0.488281E-03 0.999512 13 0.244141E-03 0.999756 14 0.122070E-03 0.999878 15 0.610352E-04 0.999939 16 0.305176E-04 0.999969 17 0.152588E-04 0.999985 18 0.762939E-05 0.999992 19 0.381470E-05 0.999996 20 0.190735E-05 0.999998 Number of coupon types is 3 BOX_NUM PDF CDF 1 0.00000 0.00000 2 0.00000 0.00000 3 0.222222 0.222222 4 0.222222 0.444444 5 0.172840 0.617284 6 0.123457 0.740741 7 0.850480E-01 0.825789 8 0.576132E-01 0.883402 9 0.387136E-01 0.922116 10 0.259107E-01 0.948026 11 0.173077E-01 0.965334 12 0.115497E-01 0.976884 13 0.770358E-02 0.984587 14 0.513698E-02 0.989724 15 0.342507E-02 0.993149 16 0.228352E-02 0.995433 17 0.152239E-02 0.996955 18 0.101494E-02 0.997970 19 0.676634E-03 0.998647 20 0.451091E-03 0.999098 Number of coupon types is 4 BOX_NUM PDF CDF 1 0.00000 0.00000 2 0.00000 0.00000 3 0.00000 0.00000 4 0.937500E-01 0.937500E-01 5 0.140625 0.234375 6 0.146484 0.380859 7 0.131836 0.512695 8 0.110229 0.622925 9 0.884399E-01 0.711365 10 0.692368E-01 0.780602 11 0.533867E-01 0.833988 12 0.407710E-01 0.874759 13 0.309441E-01 0.905703 14 0.233911E-01 0.929094 15 0.176349E-01 0.946729 16 0.132719E-01 0.960001 17 0.997682E-02 0.969978 18 0.749406E-02 0.977472 19 0.562627E-02 0.983098 20 0.422256E-02 0.987321 coupon_sample_test(): coupon_sample() samples the coupon PDF. Number of coupon types is 5 Expected wait is about 8.04719 1 24 2 17 3 12 4 11 5 12 6 5 7 8 8 12 9 18 10 16 Average wait was 13.5000 Number of coupon types is 10 Expected wait is about 23.0259 1 26 2 19 3 27 4 19 5 20 6 19 7 46 8 24 9 22 10 27 Average wait was 24.9000 Number of coupon types is 15 Expected wait is about 40.6208 1 42 2 59 3 27 4 67 5 30 6 28 7 37 8 53 9 33 10 35 Average wait was 41.1000 Number of coupon types is 20 Expected wait is about 59.9146 1 103 2 79 3 83 4 83 5 52 6 76 7 54 8 102 9 45 10 48 Average wait was 72.5000 Number of coupon types is 25 Expected wait is about 80.4719 1 119 2 90 3 120 4 68 5 113 6 86 7 81 8 73 9 82 10 83 Average wait was 91.5000 DERANGED_CDF_test(): DERANGED_CDF evaluates the Deranged CDF; DERANGED_CDF_INV inverts the Deranged CDF. DERANGED_PDF evaluates the Deranged PDF; PDF parameter A = 7 X PDF CDF CDF_INV 0 217.474 0.367857 0 1 217.591 0.735913 0 2 108.385 0.919246 0 3 36.9494 0.981746 0 4 8.21099 0.995635 0 5 2.46330 0.999802 0 6 0.00000 0.999802 0 7 0.117300 1.00000 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 = 591.191 PDF variance = 0.205928E+09 Sample size = 1000 Sample mean = 0.00000 Sample variance = 0.00000 Sample maximum = 0 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 = 0.00000 PDF parameter B = 1.00000 X PDF CDF CDF_INV 0.690015 0.490116 0.841051 0.689941 0.215023 0.633734 0.632837 0.215088 0.784071 0.435584 0.866220 0.784180 2.38193 -0.197086E-01 0.987088 2.37891 0.142470 0.636033 0.589494 0.142578 0.267333E-01 0.636619 0.517011 0.268555E-01 -0.321510E-01 0.636618 0.479546 -0.322266E-01 -0.176697 0.635263 0.389788 -0.176758 -5.41618 -0.300540E-02 0.128290E-02 -5.46875 0.279391 0.628901 0.669215 0.279297 PDF parameter A = 0.785398 PDF parameter B = 0.500000 X PDF CDF CDF_INV 0.387448 0.309379 0.548469 0.387695 -3.01065 0.304037E-01 0.941714E-01 -3.01367 -7.00808 0.679271E-02 0.435279E-01 -7.01562 2.51945 0.362866E-01 0.868899 2.52051 0.701317 0.262811 0.641340 0.701172 0.564427 0.288107 0.603213 0.564453 -0.646302 0.273735 0.261232 -0.646484 -17.1554 0.108554E-02 0.182641E-01 -17.1758 -3.52205 0.258971E-01 0.821224E-01 -3.52148 -0.768967E-01 0.318292 0.396461 -0.771484E-01 PDF parameter A = 1.57080 PDF parameter B = 0.00000 X PDF CDF CDF_INV -5.53160 0.100735E-01 0.569291E-01 -5.53906 -0.639300 0.225959 0.318940 -0.639648 -0.173669 0.308990 0.445266 -0.173828 -0.662026 0.221313 0.313858 -0.662109 3.74038 0.212342E-01 0.916844 3.73633 0.563890 0.241515 0.663435 0.563477 1.15439 0.136460 0.772773 1.15479 -0.851764 0.184474 0.275427 -0.851562 -0.189393 0.307288 0.440420 -0.189453 6.35571 0.768957E-02 0.950325 6.34766 DIPOLE_SAMPLE_test(): DIPOLE_sample() samples the Dipole distribution. PDF parameter A = 0.00000 PDF parameter B = 1.00000 Sample size = 10000 Sample mean = -0.192072E-01 Sample variance = 0.864157 Sample maximum = 8.80042 Sample minimum = -11.5394 PDF parameter A = 0.785398 PDF parameter B = 0.500000 Sample size = 10000 Sample mean = -1.06940 Sample variance = 12868.5 Sample maximum = 798.589 Sample minimum = -10945.7 PDF parameter A = 1.57080 PDF parameter B = 0.00000 Sample size = 10000 Sample mean = 1.62662 Sample variance = 14176.4 Sample maximum = 6646.72 Sample minimum = -2690.11 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 0.250000 2 0.500000 3 1.25000 PDF parameters A(1:N): PDF mean: 1 0.125000 2 0.250000 3 0.625000 PDF variance: 1 0.364583E-01 2 0.625000E-01 3 0.781250E-01 Second moments: Col 1 2 3 Row 1 0.520833E-01 0.208333E-01 0.520833E-01 2 0.208333E-01 0.125000 0.104167 3 0.520833E-01 0.104167 0.468750 Sample size = 1000 Observed Mean, Variance, Max, Min: 1 0.124714 0.356269E-01 0.983748 0.370011E-10 2 0.251260 0.641534E-01 0.995803 0.329515E-05 3 0.624026 0.793948E-01 0.999910 0.408313E-02 DIRICHLET_PDF_test(): DIRICHLET_PDF evaluates the Dirichlet PDF. Number of components N = 3 PDF parameters A: 1 0.250000 2 0.500000 3 1.25000 PDF argument X: 1 0.500000 2 0.125000 3 0.375000 PDF value = 0.639070 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 0.250000 1.50000 2 0.500000 0.500000 3 1.25000 2. Component weights 1 1.00000 2 2.00000 PDF means: 1 0.291667 2 0.166667 3 0.541667 Sample size = 1000 Observed Mean, Variance, Max, Min: 1 0.279413 0.547528E-01 0.958856 0.170654E-08 2 0.166126 0.389204E-01 0.997630 0.524259E-07 3 0.554461 0.593083E-01 0.999540 0.300963E-03 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 0.250000 1.50000 2 0.500000 0.500000 3 1.25000 2. Component weights 1 1.00000 2 2.00000 PDF argument X: 1 0.500000 2 0.125000 3 0.375000 PDF value = 2.12288 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 1.00000 2 2.00000 3 6.00000 4 2.00000 5 4.00000 6 1.00000 X PDF CDF CDF_INV 3 0.375000 0.562500 3 4 0.125000 0.687500 4 5 0.250000 0.937500 5 5 0.250000 0.937500 5 5 0.250000 0.937500 5 4 0.125000 0.687500 4 2 0.125000 0.187500 2 3 0.375000 0.562500 3 3 0.375000 0.562500 3 5 0.250000 0.937500 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 1.00000 2 2.00000 3 6.00000 4 2.00000 5 4.00000 6 1.00000 PDF mean = 3.56250 PDF variance = 1.74609 Sample size = 1000 Sample mean = 3.60200 Sample variance = 1.82342 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 = 10.0000 Y coordinate of center is B = 4.00000 Radius is C = 3.00000 Disk mean = 10.0000 4.00000 Disk variance = 4.50000 Sample size = 1000 Sample mean = 10.0151 3.93877 Sample variance = 4.50469 Sample maximum = 12.9535 6.97863 Sample minimum = 7.06840 1.09185 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 1.00000 2 1.00000 3 3.00000 4 2.00000 5 1.00000 6 2.00000 PDF parameter C: 1 0.00000 2 1.00000 3 2.00000 4 4.50000 5 6.00000 6 10.0000 X PDF CDF CDF_INV 2.00000 0.300000 0.500000 2.00000 4.50000 0.200000 0.700000 4.50000 6.00000 0.100000 0.800000 6.00000 10.0000 0.200000 1.00000 10.0000 4.50000 0.200000 0.700000 4.50000 0.00000 0.100000 0.100000 0.00000 6.00000 0.100000 0.800000 6.00000 10.0000 0.200000 1.00000 10.0000 6.00000 0.100000 0.800000 6.00000 2.00000 0.300000 0.500000 2.00000 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 1.00000 2 1.00000 3 3.00000 4 2.00000 5 1.00000 6 2.00000 PDF parameter C: 1 0.00000 2 1.00000 3 2.00000 4 4.50000 5 6.00000 6 10.0000 PDF mean = 4.20000 PDF variance = 11.3100 Sample size = 1000 Sample mean = 4.04600 Sample variance = 10.7366 Sample maximum = 10.0000 Sample minimum = 0.00000 ENGLISH_LETTER_CDF_test(): ENGLISH_LETTER_CDF evaluates the English Letter CDF; ENGLISH_LETTER_CDF_INV inverts the English Letter CDF. ENGLISH_LETTER_PDF evaluates the English Letter PDF; C PDF CDF CDF_INV "e" 0.127020 0.293960 "e" "w" 0.023610 0.978020 "w" "p" 0.019290 0.702400 "p" "a" 0.081670 0.081670 "a" "c" 0.027820 0.124410 "c" "i" 0.069660 0.466990 "i" "i" 0.069660 0.466990 "i" "p" 0.019290 0.702400 "p" "r" 0.059870 0.763220 "r" "h" 0.060940 0.397330 "h" 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 0.379681E-01 0.341262 12 15 0.352618E-01 0.450896 15 38 0.765777E-02 0.928464 38 18 0.331269E-01 0.553935 18 14 0.375972E-01 0.415634 14 10 0.354122E-01 0.267591 10 19 0.333674E-01 0.587303 19 31 0.151552E-01 0.856106 31 24 0.253187E-01 0.726295 24 23 0.265316E-01 0.700976 23 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 = 19.3890 Sample variance = 138.156 Sample maximum = 73 Sample minimum = 1 ENGLISH_WORD_LENGTH_CDF_test(): ENGLISH_WORD_LENGTH_CDF evaluates the English Word Length CDF; ENGLISH_WORD_LENGTH_CDF_INV inverts the English Word Length CDF. ENGLISH_WORD_LENGTH_PDF evaluates the English Word Length PDF; X PDF CDF CDF_INV 13 0.483014E-02 0.995110 13 2 0.169755 0.201356 2 2 0.169755 0.201356 2 3 0.211926 0.413282 3 9 0.403212E-01 0.937628 9 3 0.211926 0.413282 3 2 0.169755 0.201356 2 11 0.158205E-01 0.981109 11 2 0.169755 0.201356 2 3 0.211926 0.413282 3 ENGLISH_WORD_LENGTH_SAMPLE_test(): ENGLISH_WORD_LENGTH_mean() computes the English Word Length mean; ENGLISH_WORD_LENGTH_sample() samples the English Word Length distribution; ENGLISH_WORD_LENGTH_variance() computes the English Word Length variance. PDF mean = 4.73912 PDF variance = 7.05635 Sample size = 1000 Sample mean = 4.79100 Sample variance = 7.13646 Sample maximum = 18 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3 X PDF CDF CDF_INV 8.09136 0.261622 0.687519 8.09180 4.15613 0.370723 0.210989 4.15625 2.47702 0.187986 0.389934E-01 2.47656 8.58302 0.233957 0.729730 8.58203 3.62748 0.334668 0.146064 3.62695 6.57954 0.344905 0.528104 6.58008 2.26852 0.153895 0.266349E-01 2.26953 3.32193 0.304496 0.112160 3.32227 6.91353 0.327847 0.567054 6.91406 12.8480 0.677037E-01 0.934553 12.8516 ERLANG_SAMPLE_test(): ERLANG_mean() computes the Erlang mean; ERLANG_sample() samples the Erlang distribution; ERLANG_variance() computes the Erlang variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3 PDF mean = 7.00000 PDF variance = 12.0000 Sample size = 1000 Sample mean = 7.11275 Sample variance = 11.6923 Sample maximum = 23.5907 Sample minimum = 1.16698 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 = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 4.13580 0.104241 0.791517 4.13580 10.2838 0.481958E-02 0.990361 10.2838 1.17092 0.459045 0.819109E-01 1.17092 1.15274 0.463237 0.735263E-01 1.15274 1.39301 0.410798 0.178405 1.39301 3.06129 0.178388 0.643223 3.06129 1.46423 0.396427 0.207146 1.46423 2.98024 0.185766 0.628468 2.98024 3.31345 0.157257 0.685485 3.31345 2.13516 0.283448 0.433105 2.13516 EXPONENTIAL_SAMPLE_test(): EXPONENTIAL_mean() computes the Exponential mean; EXPONENTIAL_sample() samples the Exponential distribution; EXPONENTIAL_variance() computes the Exponential variance. PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF mean = 11.0000 PDF variance = 100.000 Sample size = 1000 Sample mean = 11.3115 Sample variance = 101.966 Sample maximum = 73.6863 Sample minimum = 1.01381 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 0.951172 0.386288 0.613712 0.951172 0.529339E-01 0.948443 0.515573E-01 0.529339E-01 1.67229 0.187817 0.812183 1.67229 0.153804 0.857440 0.142560 0.153804 1.33517 0.263115 0.736885 1.33517 0.271450 0.762273 0.237727 0.271450 0.935259 0.392484 0.607516 0.935259 1.94509 0.142974 0.857026 1.94509 0.878468 0.415419 0.584581 0.878468 2.80002 0.608091E-01 0.939191 2.80002 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 = 1.00000 PDF variance = 1.00000 Sample size = 1000 Sample mean = 0.937178 Sample variance = 0.754817 Sample maximum = 6.19913 Sample minimum = 0.639169E-03 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 = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV -0.730878E-01 0.904144E-01 0.135909 -0.730878E-01 9.83042 0.227708E-01 0.929114 9.83042 2.65616 0.119926 0.447738 2.65616 3.18384 0.114502 0.509696 3.18384 4.93426 0.860585E-01 0.686581 4.93426 1.74202 0.122161 0.336284 1.74202 -3.38922 0.484329E-02 0.241041E-02 -3.38922 9.56248 0.247277E-01 0.922753 9.56248 5.44653 0.769608E-01 0.728328 5.44653 1.07121 0.116264 0.255924 1.07121 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 = 2.00000 PDF parameter B = 3.00000 PDF mean = 3.73165 PDF variance = 14.8044 Sample size = 1000 Sample mean = 3.77229 Sample variance = 14.3312 Sample maximum = 27.7111 Sample minimum = -3.90885 F_CDF_test(): F_CDF evaluates the F CDF. F_PDF evaluates the F PDF. F_sample() samples the F PDF. PDF parameter M = 1 PDF parameter N = 1 X PDF CDF 1.04930 0.151633 0.507658 2.06603 0.722280E-01 0.613034 0.827866 0.191393 0.469980 0.368887E-01 1.59835 0.120801 6.32734 0.172700E-01 0.759109 4.53904 0.269733E-01 0.720621 5.18315 0.226122E-01 0.736522 0.619087 0.249864 0.424404 93.3004 0.349458E-03 0.934326 0.458722 0.322183 0.378993 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 = 1.50000 PDF variance = 3.37500 Sample size = 1000 Sample mean = 1.58536 Sample variance = 4.26003 Sample maximum = 37.0674 Sample minimum = 0.890829E-01 FERMI_DIRAC_SAMPLE_test(): FERMI_DIRAC_sample() samples the Fermi Dirac distribution. U = 1.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 0.596973 Sample variance = 0.179617 Maximum value = 2.68615 Minimum value = 0.855785E-04 U = 2.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 1.05695 Sample variance = 0.436688 Maximum value = 3.55226 Minimum value = 0.746845E-05 U = 4.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 2.03106 Sample variance = 1.40021 Maximum value = 5.72374 Minimum value = 0.928487E-04 U = 8.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 3.98218 Sample variance = 5.35826 Maximum value = 9.39904 Minimum value = 0.438916E-03 U = 16.0000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 7.99966 Sample variance = 21.4497 Maximum value = 17.1042 Minimum value = 0.274701E-02 U = 32.0000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 15.9909 Sample variance = 85.6300 Maximum value = 33.1720 Minimum value = 0.887337E-02 U = 1.00000 V = 0.250000 SAMPLE_NUM = 10000 Sample mean = 0.503992 Sample variance = 0.904084E-01 Maximum value = 1.38260 Minimum value = 0.932658E-04 FISHER_PDF_test(): FISHER_PDF evaluates the Fisher PDF. PDF parameters: Concentration parameter KAPPA = 0.00000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF 0.3215 0.8995 0.2959 0.795775E-01 -0.2637 -0.5532 0.7902 0.795775E-01 0.5099 -0.8599 -0.0261 0.795775E-01 -0.6289 -0.7587 -0.1696 0.795775E-01 0.5052 -0.8086 0.3015 0.795775E-01 -0.4874 -0.0196 -0.8730 0.795775E-01 0.0405 -0.8262 0.5619 0.795775E-01 0.8142 -0.5670 0.1247 0.795775E-01 -0.7368 -0.3006 0.6057 0.795775E-01 -0.1706 0.2514 -0.9527 0.795775E-01 PDF parameters: Concentration parameter KAPPA = 0.500000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF 0.1299 -0.8630 0.4882 0.814805E-01 0.8677 0.1510 0.4735 0.117833 0.2828 0.7846 0.5518 0.879518E-01 0.2166 0.6473 0.7308 0.850887E-01 0.4916 -0.2291 0.8402 0.976301E-01 0.0689 -0.3542 -0.9326 0.790341E-01 -0.8643 -0.4943 -0.0926 0.495631E-01 0.9614 0.1242 0.2455 0.123484 0.1832 0.3258 -0.9275 0.836820E-01 0.7306 -0.1147 0.6731 0.110025 PDF parameters: Concentration parameter KAPPA = 10.0000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF 0.8531 0.4855 0.1910 0.366306 0.9891 -0.1383 0.0500 1.42750 0.9791 0.1975 -0.0474 1.29200 0.9319 0.3374 0.1332 0.805372 0.9209 -0.2138 -0.3260 0.721434 0.7915 -0.3510 -0.5003 0.197896 0.8872 0.0841 0.4537 0.515172 0.7540 0.3155 -0.5761 0.136038 0.9553 0.2801 -0.0945 1.01788 0.9858 -0.1249 -0.1124 1.38072 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 2.80444 0.405895 0.423433 2.80444 2.30696 0.391539 0.218176 2.30696 2.13098 0.344006 0.153140 2.13098 5.97747 0.344811E-01 0.939079 5.97747 4.68844 0.964617E-01 0.862495 4.68844 1.88826 0.250132 0.805488E-01 1.88826 2.25711 0.380293 0.198930 2.25711 2.49942 0.417305 0.296460 2.49942 2.21032 0.368093 0.181414 2.21032 2.70119 0.415880 0.380963 2.70119 FISK_SAMPLE_test(): FISK_mean() computes the Fisk mean; FISK_sample() samples the Fisk distribution; FISK_variance() computes the Fisk variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF mean = 3.41840 PDF variance = 3.82494 Sample size = 1000 Sample mean = 3.35985 Sample variance = 2.41661 Sample maximum = 16.1012 Sample minimum = 1.12321 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 = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 6.59988 0.432313E-01 0.935324 6.60038 1.65955 0.195320 0.343563 1.65960 2.26094 0.180978 0.456899 2.26081 3.25001 0.150683 0.621482 3.24946 0.256227 0.212534 0.545306E-01 0.256267 1.60091 0.196514 0.332075 1.60087 0.645259 0.210239 0.136830 0.645233 0.685461E-02 0.212965 0.145979E-02 0.685470E-02 0.381587 0.212009 0.811431E-01 0.381643 1.12361 0.204761 0.236203 1.12348 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 = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.90672 PDF variance = 4.55099 Sample size = 1000 Sample mean = 3.06313 Sample variance = 4.59828 Sample maximum = 11.3386 Sample minimum = 0.293263E-02 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 = 3.00000 X PDF CDF CDF_INV 1.17457 0.850349 0.539502 1.17457 1.09807 0.969586 0.469877 1.09807 1.06818 1.01441 0.440226 1.06818 1.22087 0.779449 0.577219 1.22087 1.15063 0.887745 0.518700 1.15063 1.96338 0.176897 0.876232 1.96338 0.592674 0.199413 0.820158E-02 0.592674 0.959076 1.14134 0.321889 0.959076 1.13858 0.906629 0.507888 1.13858 0.741692 0.854685 0.862144E-01 0.741692 FRECHET_SAMPLE_test(): FRECHET_mean() computes the Frechet mean; FRECHET_sample() samples the Frechet distribution; FRECHET_variance() computes the Frechet variance. PDF parameter ALPHA = 3.00000 PDF mean = 1.35412 PDF variance = 0.845303 Sample size = 1000 Sample mean = 1.35470 Sample variance = 0.654175 Sample maximum = 10.1040 Sample minimum = 0.530314 GAMMA_CDF_test(): GAMMA_CDF evaluates the Gamma CDF. GAMMA_PDF evaluates the Gamma PDF. PDF parameter A = 1.00000 PDF parameter B = 1.50000 PDF parameter C = 3.00000 X PDF CDF 4.31820 0.178560 0.380538 2.83378 0.146709 0.125433 2.73852 0.140509 0.111749 7.69656 0.764799E-01 0.822375 8.62233 0.534541E-01 0.882051 8.68157 0.521860E-01 0.885180 3.52043 0.175350 0.237581 7.77728 0.742307E-01 0.828457 3.56733 0.176336 0.245830 1.82778 0.584598E-01 0.186261E-01 GAMMA_SAMPLE_test(): GAMMA_mean() computes the Gamma mean; GAMMA_sample() samples the Gamma distribution; GAMMA_variance() computes the Gamma variance. PDF parameter A = 1.00000 PDF parameter B = 3.00000 PDF parameter C = 2.00000 PDF mean = 7.00000 PDF variance = 18.0000 Sample size = 1000 Sample mean = 6.97509 Sample variance = 17.9087 Sample maximum = 30.3563 Sample minimum = 1.07897 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 2.74579 0.155100 0.350921 2.74579 4.14626 0.146384 0.568135 4.14626 3.15057 0.158171 0.414495 3.15057 1.64682 0.122974 0.195269 1.64682 7.64769 0.468923E-01 0.899297 7.64769 4.79194 0.128715 0.657221 4.79194 5.83299 0.950902E-01 0.773814 5.83299 2.87888 0.156668 0.371674 2.87888 3.58600 0.156049 0.483099 3.58600 2.89076 0.156781 0.373536 2.89076 GENLOGISTIC_SAMPLE_test(): GENLOGISTIC_mean() computes the Genlogistic mean; GENLOGISTIC_sample() samples the Genlogistic distribution; GENLOGISTIC_variance() computes the Genlogistic variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF mean = 4.00000 PDF variance = 8.15947 Sample size = 1000 Sample mean = 3.86450 Sample variance = 7.68272 Sample maximum = 15.4713 Sample minimum = -4.06744 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 = 0.250000 X PDF CDF CDF_INV 7 0.444946E-01 0.866516 8 5 0.791016E-01 0.762695 6 1 0.250000 0.250000 2 13 0.791909E-02 0.976243 14 1 0.250000 0.250000 2 13 0.791909E-02 0.976243 14 2 0.187500 0.437500 3 4 0.105469 0.683594 5 3 0.140625 0.578125 4 2 0.187500 0.437500 3 GEOMETRIC_SAMPLE_test(): GEOMETRIC_mean() computes the Geometric mean; GEOMETRIC_sample() samples the Geometric distribution; GEOMETRIC_variance() computes the Geometric variance. PDF parameter A = 0.250000 PDF mean = 4.00000 PDF variance = 12.0000 Sample size = 1000 Sample mean = 3.92500 Sample variance = 10.8382 Sample maximum = 26 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 = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 0.209653 1.76293 0.491838 0.209653 0.133724E-01 2.90833 0.395024E-01 0.133724E-01 0.171698 1.95546 0.421315 0.171698 0.458928 0.815269 0.802290 0.458928 0.233800E-01 2.84086 0.682693E-01 0.233800E-01 0.516243 0.666570 0.844647 0.516243 0.481982 0.752702 0.820357 0.481982 0.814249E-01 2.46885 0.222211 0.814249E-01 0.387650 1.03369 0.736625 0.387650 0.404010E-01 2.72836 0.115662 0.404010E-01 GOMPERTZ_SAMPLE_test(): GOMPERTZ_sample() samples the Gompertz distribution; PDF parameter A = 2.00000 PDF parameter B = 3.00000 Sample size = 1000 Sample mean = 0.278930 Sample variance = 0.580855E-01 Sample maximum = 1.55424 Sample minimum = 0.605413E-03 GUMBEL_CDF_test(): GUMBEL_CDF evaluates the Gumbel CDF. GUMBEL_CDF_INV inverts the Gumbel CDF. GUMBEL_PDF evaluates the Gumbel PDF. X PDF CDF CDF_INV 0.531164 0.326579 0.555481 0.531164 -0.204829 0.359700 0.293078 -0.204829 -0.995546 0.180747 0.667901E-01 -0.995546 1.34899 0.200189 0.771435 1.34899 -0.351744E-01 0.367649 0.354942 -0.351744E-01 0.803099 0.286208 0.638944 0.803099 -0.162622 0.362776 0.308328 -0.162622 -0.360241 0.341833 0.238431 -0.360241 0.155725 0.363666 0.424946 0.155725 -0.258913 0.354656 0.273755 -0.258913 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 = 0.577210 Sample variance = 1.42912 Sample maximum = 8.15699 Sample minimum = -2.01182 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 = 0.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 1.23791 0.329397 0.464055 1.23791 1.27558 0.325521 0.476390 1.27558 3.12042 0.118119 0.881290 3.12042 0.481682 0.387538 0.190322 0.481682 1.33934 0.318808 0.496931 1.33934 0.510098 0.386175 0.201315 0.510098 3.36256 0.970735E-01 0.907291 3.36256 2.84579 0.144966 0.845234 2.84579 0.674599 0.376882 0.264109 0.674599 0.543431 0.384484 0.214159 0.543431 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 = 0.00000 PDF parameter B = 10.0000 PDF mean = 7.97885 PDF variance = 36.3380 Sample size = 1000 Sample mean = 8.01778 Sample variance = 37.0183 Sample maximum = 34.2023 Sample minimum = 0.406274E-03 HYPERGEOMETRIC_CDF_test(): HYPERGEOMETRIC_CDF evaluates the Hypergeometric CDF. HYPERGEOMETRIC_PDF evaluates the Hypergeometric PDF. Total number of balls = 100 Number of white balls = 7 Number of balls taken = 10 PDF argument X = 7 PDF value = = 0.749646E-08 CDF value = = 1.00000 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 = 0.700000 PDF variance = 0.591818 Sample size = 1000 Sample mean = 0.686000 Sample variance = 0.563968 Sample maximum = 3 Sample minimum = 0 I4_CHOOSE_test(): I4_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 I4_CHOOSE_LOG_test(): I4_CHOOSE_LOG evaluates log(C(N,K)). N K lcnk elcnk CNK 0 0 0.00000 1.00000 1 1 0 0.00000 1.00000 1 1 1 0.00000 1.00000 1 2 0 0.00000 1.00000 1 2 1 0.693147 2.00000 2 2 2 0.00000 1.00000 1 3 0 0.00000 1.00000 1 3 1 1.09861 3.00000 3 3 2 1.09861 3.00000 3 3 3 0.00000 1.00000 1 4 0 0.00000 1.00000 1 4 1 1.38629 4.00000 4 4 2 1.79176 6.00000 6 4 3 1.38629 4.00000 4 4 4 0.00000 1.00000 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 F 98 F 99 F 100 T 101 F 102 F 103 F I4_UNIFORM_AB_test(): I4_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 1 39 2 28 3 -29 4 -26 5 -26 6 18 7 81 8 -22 9 -82 10 67 11 15 12 166 13 -53 14 60 15 -20 16 -9 17 -68 18 15 19 64 20 -96 I4VEC_UNIFORM_AB_test(): I4VEC_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The random vector: 1 -40 2 12 3 -6 4 -70 5 178 6 187 7 -66 8 60 9 141 10 84 11 51 12 43 13 110 14 11 15 184 16 192 17 38 18 178 19 -72 20 -64 I4VEC_UNIQUE_COUNT_test(): I4VEC_UNIQUE_COUNT counts unique entries in an I4VEC. Input vector: 1 9 2 13 3 12 4 20 5 17 6 6 7 20 8 12 9 10 10 2 11 5 12 15 13 0 14 3 15 10 16 7 17 17 18 18 19 11 20 10 Number of unique entries is 15 INVERSE_GAUSSIAN_CDF_test(): INVERSE_GAUSSIAN_CDF evaluates the Inverse Gaussian CDF. INVERSE_GAUSSIAN_PDF evaluates the Inverse Gaussian PDF. PDF parameter A = 5.00000 PDF parameter B = 2.00000 X PDF CDF 35.6995 0.920066E-03 0.987041 1.29726 0.250201 0.310070 0.647531 0.335978 0.115480 10.2624 0.154054E-01 0.876757 3.61181 0.804579E-01 0.640668 1.86570 0.179346 0.430764 8.61718 0.209894E-01 0.847151 1.03346 0.292090 0.238613 1.88896 0.177045 0.434908 0.953096 0.304940 0.214620 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 = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 2.66667 Sample size = 1000 Sample mean = 2.01692 Sample variance = 2.94078 Sample maximum = 15.2775 Sample minimum = 0.208871 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 = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 0.558058 0.200435 0.400870 0.558058 -2.69278 0.394514E-01 0.789028E-01 -2.69278 2.05577 0.147463 0.705075 2.05577 -0.706326E-01 0.146371 0.292742 -0.706326E-01 -0.847104 0.992765E-01 0.198553 -0.847104 2.89669 0.968455E-01 0.806309 2.89669 0.962654 0.245375 0.490750 0.962654 0.609143 0.205621 0.411241 0.609143 2.19339 0.137657 0.724686 2.19339 10.3728 0.230492E-02 0.995390 10.3728 LAPLACE_SAMPLE_test(): LAPLACE_mean() computes the Laplace mean; LAPLACE_sample() samples the Laplace distribution; LAPLACE_variance() computes the Laplace variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF mean = 1.00000 PDF variance = 8.00000 Sample size = 1000 Sample mean = 1.05367 Sample variance = 9.31911 Sample maximum = 17.0564 Sample minimum = -15.4737 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 = 1.00000 PDF parameter B = 2.00000 X PDF CDF X2 27.1414 0.406273E-02 0.782088 27.1414 4.04973 0.763183E-01 0.418048 4.04973 141.509 0.336340E-03 0.905033 141.509 3.88096 0.815405E-01 0.404735 3.88096 11.6941 0.146925E-01 0.665410 11.6941 17.3322 0.804016E-02 0.726385 17.3322 36.6777 0.257429E-02 0.812839 36.6777 1.73244 0.229787 0.984426E-01 1.73244 10.7500 0.167253E-01 0.650613 10.7500 99.0236 0.575438E-03 0.886417 99.0236 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 = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 0.532995E-01 0.118252 0.383824 0.532995E-01 4.43254 0.645706E-01 0.847648 4.43254 3.26224 0.922203E-01 0.756046 3.26224 -1.19005 0.939180E-01 0.250673 -1.19005 1.82534 0.119826 0.601728 1.82534 4.16782 0.706300E-01 0.829758 4.16782 2.04842 0.116791 0.628131 2.04842 3.08719 0.963096E-01 0.739543 3.08719 0.346695 0.121724 0.419055 0.346695 -2.67566 0.592274E-01 0.137308 -2.67566 LOGISTIC_SAMPLE_test(): LOGISTIC_mean() computes the Logistic mean; LOGISTIC_sample() samples the Logistic distribution; LOGISTIC_variance() computes the Logistic variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 29.6088 Sample size = 1000 Sample mean = 2.05671 Sample variance = 32.8427 Sample maximum = 25.7276 Sample minimum = -18.9369 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 = 10.0000 PDF parameter B = 2.25000 X PDF CDF CDF_INV 177671. 0.648876E-06 0.823261 177671. 23600.6 0.750931E-05 0.512237 23600.6 30641.2 0.572464E-05 0.558320 30641.2 167899. 0.702629E-06 0.816662 167899. 1378.91 0.602351E-04 0.109062 1378.91 111488. 0.122659E-05 0.764466 111488. 6859.08 0.225985E-04 0.302047 6859.08 11430.3 0.148667E-04 0.385316 11430.3 2730.81 0.422178E-04 0.176745 2730.81 71660.9 0.215651E-05 0.699969 71660.9 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 = 1.00000 PDF parameter B = 2.00000 PDF mean = 20.0855 PDF variance = 21623.0 Sample size = 1000 Sample mean = 25.2862 Sample variance = 25807.6 Sample maximum = 3043.81 Sample minimum = 0.104009E-01 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 = 0.250000 X PDF CDF CDF_INV 2 0.108627 0.977642 3 1 0.869015 0.869015 2 3 0.181045E-01 0.995746 4 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 LOG_SERIES_SAMPLE_test(): LOG_SERIES_mean() computes the Log Series mean; LOG_SERIES_variance() computes the Log Series variance; LOG_SERIES_sample() samples the Log Series distribution. PDF parameter A = 0.250000 PDF mean = 1.15869 PDF variance = 0.202361 Sample size = 1000 Sample mean = 1.16200 Sample variance = 0.233990 Sample maximum = 6 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 = 2.00000 PDF parameter B = 20.0000 X PDF CDF CDF_INV 11.0185 0.394149E-01 0.741094 11.0185 3.23073 0.134426 0.208271 3.23073 3.63239 0.119562 0.259163 3.63239 2.89213 0.150164 0.160188 2.89213 17.7649 0.244468E-01 0.948532 17.7649 6.62039 0.655995E-01 0.519853 6.62039 9.47910 0.458160E-01 0.675737 9.47910 7.51364 0.578008E-01 0.574820 7.51364 15.5140 0.279938E-01 0.889693 15.5140 4.55702 0.953023E-01 0.357651 4.55702 LOG_UNIFORM_SAMPLE_test(): LOG_UNIFORM_mean() computes the Log Uniform mean; LOG_UNIFORM_sample() samples the Log Uniform distribution; PDF parameter A = 2.00000 PDF parameter B = 20.0000 PDF mean = 7.81730 Sample size = 1000 Sample mean = 7.91145 Sample variance = 24.6553 Sample maximum = 19.9654 Sample minimum = 2.00223 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 -7.24918 0.594409E-02 0.436344E-01 -7.24918 1.91572 0.681611E-01 0.846864 1.91572 -0.414100 0.271716 0.375031 -0.414100 -26.5773 0.450003E-03 0.119711E-01 -26.5773 27.7945 0.411502E-03 0.988553 27.7945 0.305703 0.291105 0.594437 0.305703 -0.470456 0.260626 0.360028 -0.470456 -0.580087 0.238167 0.332681 -0.580087 4.14706 0.174914E-01 0.924682 4.14706 0.332599 0.286605 0.602206 0.332599 LORENTZ_SAMPLE_test(): LORENTZ_mean() computes the Lorentz mean; LORENTZ_variance() computes the Lorentz variance; LORENTZ_sample() samples the Lorentz distribution. PDF mean = 0.00000 PDF variance = 0.179769+309 Sample size = 1000 Sample mean = -0.468379 Sample variance = 871.155 Sample maximum = 527.629 Sample minimum = -501.360 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 = 2.00000 X PDF CDF CDF_INV 3.07861 0.289093 0.620338 3.07812 4.15571 0.198889 0.754867 4.15625 5.45266 0.721174E-01 0.858502 5.45312 2.21082 0.264617 0.470180 2.21094 3.43538 0.269225 0.670760 3.43555 3.05971 0.289726 0.617489 3.05957 1.89830 0.229063 0.406218 1.89844 5.76808 0.518499E-01 0.876545 5.76953 5.64392 0.592607E-01 0.869721 5.64453 2.13260 0.256905 0.454654 2.13281 MAXWELL_SAMPLE_test(): MAXWELL_mean() computes the Maxwell mean; MAXWELL_variance() computes the Maxwell variance; MAXWELL_sample() samples the Maxwell distribution. PDF parameter A = 2.00000 PDF mean = 3.19154 PDF mean = 1.81408 Sample size = 1000 Sample mean = 3.20057 Sample variance = 1.73355 Sample maximum = 9.54369 Sample minimum = 0.353793 MULTINOMIAL_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_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 = 1 0.125000 2 0.500000 3 0.375000 PDF means: 1 0.625000 2 2.50000 3 1.87500 PDF variances: 1 0.546875 2 1.25000 3 1.17188 Sample size = 1000 Component Mean, Variance, Min, Max: 1 0.613000 0.551783 0 4 2 2.48700 1.32115 0 5 3 1.90000 1.19119 0 5 MULTINOMIAL_PDF_test(): MULTINOMIAL_PDF evaluates the Multinomial PDF. PDF parameter A = 5 PDF parameter B = 3 PDF parameter C: 1 0.100000 2 0.500000 3 0.400000 PDF argument X: 0 2 3 PDF value = 0.160000 MULTINOULLI_PDF_test(): MULTINOULLI_PDF evaluates the Multinoulli PDF. X pdf(X) 0 0.00000 1 0.273809 2 0.282770 3 0.347725E-01 4 0.271326 5 0.137323 6 0.00000 NAKAGAMI_CDF_test(): NAKAGAMI_CDF evaluates the Nakagami CDF; NAKAGAMI_PDF evaluates the Nakagami PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 3.18257 0.586699 0.692394 3.18258 3.25820 0.540746 0.735053 3.25820 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 0.825480 3.44721 3.48305 0.390724 0.839911 3.48305 3.51640 0.368580 0.852572 3.51640 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 = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 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 = 0.250000 X PDF CDF CDF_INV 4 0.105469 0.261719 4 5 0.105469 0.367188 5 10 0.563135E-01 0.755975 10 2 0.625000E-01 0.625000E-01 2 5 0.105469 0.367188 5 5 0.105469 0.367188 5 11 0.469279E-01 0.802903 11 9 0.667419E-01 0.699661 9 6 0.988770E-01 0.466064 6 8 0.778656E-01 0.632919 8 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 = 0.750000 PDF mean = 2.66667 PDF variance = 0.888889 Sample size = 1000 Sample mean = 2.67100 Sample variance = 0.831591 Sample maximum = 7 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 0.2034309459874338 0.390772 0.580601 0.2034309459958507 0.6273341135979413 0.327682 0.734780 0.6273341136078929 -0.5510600328324856E-01 0.398337 0.478027 -0.5510600328879422E-01 -1.502331834538291 0.129065 0.665057E-01 -1.502331834553144 -0.7646259777083441 0.297820 0.222247 -0.7646259777153389 -0.6652765282044870 0.319744 0.252937 -0.6652765282156468 1.117207002521104 0.213736 0.868047 1.117207002534704 1.277951319784603 0.176309 0.899367 1.277951319800988 0.8434167781170865 0.279539 0.800502 0.8434167781191150 -0.3750422906187268 0.371849 0.353815 -0.3750422906141146 NORMAL_01_SAMPLES_test(): NORMAL_01_mean() computes the Normal 01 mean; NORMAL_01_SAMPLES samples the Normal 01 PDF; NORMAL_01_VARIANCE returns the Normal 01 variance. PDF mean = 0.00000 PDF variance = 1.00000 Sample size = 1000 Sample mean = -0.291874E-02 Sample variance = 1.04962 Sample maximum = 3.05501 Sample minimum = -3.91804 NORMAL_CDF_test(): NORMAL_CDF evaluates the Normal CDF; NORMAL_CDF_INV inverts the Normal CDF. NORMAL_PDF evaluates the Normal PDF; PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 X PDF CDF CDF_INV 96.7626 0.259839E-01 0.414561 96.7626 120.567 0.103895E-01 0.914829 120.567 91.5910 0.227288E-01 0.287536 91.5910 102.476 0.262363E-01 0.565548 102.476 87.7210 0.190242E-01 0.206507 87.7210 76.5336 0.782285E-02 0.588585E-01 76.5336 110.516 0.208010E-01 0.758378 110.516 116.677 0.143352E-01 0.866888 116.677 90.1344 0.214233E-01 0.255363 90.1344 112.025 0.192868E-01 0.788630 112.025 NORMAL_SAMPLES_test(): NORMAL_mean() computes the Normal mean; NORMAL_SAMPLES samples the Normal distribution; NORMAL_VARIANCE returns the Normal variance. PDF parameter MU = 100.000 PDF parameter SIGMA = 15.0000 PDF mean = 100.000 PDF variance = 225.000 Sample size = 1000 Sample mean = 100.133 Sample variance = 211.467 Sample maximum = 148.744 Sample minimum = 53.3664 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 = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [ 50.0000 , 150.000 ] X PDF CDF CDF_INV 141.040 0.434528E-02 0.971098 141.040 73.1046 0.937287E-02 0.123892 73.1046 85.5496 0.141464E-01 0.271217 85.5496 119.024 0.125155E-01 0.789853 119.024 86.2689 0.143776E-01 0.281476 86.2689 136.213 0.585550E-02 0.946586 136.213 143.876 0.358369E-02 0.982321 143.876 113.976 0.142999E-01 0.722033 113.976 62.9038 0.556005E-02 0.483757E-01 62.9038 71.8439 0.886664E-02 0.112395 71.8439 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 = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [ 50.0000 , 150.000 ] PDF mean = 100.000 PDF variance = 483.588 Sample size = 1000 Sample mean = 99.5066 Sample variance = 504.987 Sample maximum = 149.383 Sample minimum = 50.6490 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 = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [ 50.0000 ,+oo] X PDF CDF CDF_INV 95.8778 0.161087E-01 0.421352 95.8778 77.6074 0.109333E-01 0.166238 77.6074 100.763 0.163216E-01 0.500821 100.763 106.660 0.157600E-01 0.595835 106.660 88.6996 0.147434E-01 0.309930 88.6996 83.8320 0.132478E-01 0.241655 83.8320 156.253 0.129879E-02 0.987495 156.253 57.7747 0.392190E-02 0.233907E-01 57.7747 103.111 0.162033E-01 0.539023 103.111 114.072 0.139368E-01 0.706567 114.072 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 = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [ 50.0000 ,+oo] PDF mean = 101.381 PDF variance = 554.032 Sample size = 1000 Sample mean = 101.383 Sample variance = 557.713 Sample maximum = 182.603 Sample minimum = 50.3059 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 = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [-oo, 150.000 ] X PDF CDF CDF_INV 108.706 0.153685E-01 0.650981 108.706 82.9576 0.129436E-01 0.253483 82.9576 103.517 0.161684E-01 0.568887 103.517 116.313 0.131979E-01 0.760267 116.313 103.241 0.161925E-01 0.564421 103.241 86.4665 0.141036E-01 0.300984 86.4665 116.489 0.131370E-01 0.762587 116.489 99.7356 0.163283E-01 0.507323 99.7356 139.968 0.454942E-02 0.967059 139.968 76.7253 0.105866E-01 0.180026 76.7253 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 = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [-oo, 150.000 ] PDF mean = 98.6188 PDF variance = 554.032 Sample size = 1000 Sample mean = 98.5699 Sample variance = 566.649 Sample maximum = 149.396 Sample minimum = 21.5108 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 = 0.500000 PDF parameter B = 5.00000 X PDF CDF CDF_INV 0.501175 9.86018 0.116655E-01 0.501175 0.664242 1.81913 0.758332 0.664242 0.761332 0.802373 0.877826 0.761332 0.509703 8.91084 0.916246E-01 0.509703 0.588009 3.78019 0.555442 0.588009 0.630856 2.47879 0.687249 0.630856 0.632960 2.42976 0.692411 0.632960 0.620906 2.72687 0.661374 0.620906 0.854776 0.400594 0.931516 0.854776 0.502510 9.70404 0.247252E-01 0.502510 PARETO_SAMPLE_test(): PARETO_mean() computes the Pareto mean; PARETO_sample() samples the Pareto distribution; PARETO_variance() computes the Pareto variance. PDF parameter A = 0.500000 PDF parameter B = 5.00000 PDF mean = 0.625000 PDF variance = 0.260417E-01 Sample size = 1000 Sample mean = 0.622116 Sample variance = 0.241939E-01 Sample maximum = 2.02993 Sample minimum = 0.500023 PEARSON_05_PDF_test(): PEARSON_05_PDF evaluates the Pearson 05 PDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF argument X = 5.00000 PDF value = 0.758163E-01 PLANCK_PDF_test(): PLANCK_PDF evaluates the Planck PDF. PLANCK_sample() samples the Planck PDF. PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF 1.29319 0.433854 0.710596 0.281362 6.75673 0.102802E-02 1.11213 0.410962 0.613702 0.236071 3.07345 0.153410 1.99577 0.368585 2.01079 0.365609 3.10060 0.149171 2.38193 0.286552 PLANCK_SAMPLE_test(): PLANCK_mean() computes the Planck mean. PLANCK_sample() samples the Planck distribution. PLANCK_variance() computes the Planck variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 3.83223 PDF variance = 4.11326 Sample size = 1000 Sample mean = 1.88664 Sample variance = 1.04129 Sample maximum = 7.56310 Sample minimum = 0.299437E-01 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 = 10.0000 X PDF CDF CDF_INV 8 0.112599 0.332820 8 8 0.112599 0.332820 8 8 0.112599 0.332820 8 5 0.378333E-01 0.670860E-01 5 10 0.125110 0.583040 10 15 0.347181E-01 0.951260 15 13 0.729079E-01 0.864464 13 16 0.216988E-01 0.972958 16 11 0.113736 0.696776 11 18 0.709111E-02 0.992813 18 POISSON_SAMPLE_test(): POISSON_mean() computes the Poisson mean; POISSON_sample() samples the Poisson distribution; POISSON_variance() computes the Poisson variance. PDF parameter A = 10.0000 PDF mean = 10.0000 PDF variance = 10.0000 Sample size = 1000 Sample mean = 9.96800 Sample variance = 10.0370 Sample maximum = 21 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 = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 1.81557 0.403461 0.366257 1.81557 2.88911 0.642025 0.927441 2.88911 2.52940 0.562089 0.710873 2.52940 2.89349 0.642998 0.930255 2.89349 2.36214 0.524920 0.619967 2.36214 1.13295 0.251767 0.142620 1.13295 2.86455 0.636566 0.911736 2.86455 2.98711 0.663801 0.991422 2.98711 2.59736 0.577191 0.749585 2.59736 1.09064 0.242364 0.132166 1.09064 POWER_SAMPLE_test(): POWER_mean() computes the Power mean; POWER_sample() samples the Power distribution; POWER_variance() computes the Power variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 0.500000 Sample size = 1000 Sample mean = 1.94810 Sample variance = 0.527472 Sample maximum = 2.99790 Sample minimum = 0.772063E-01 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 = 0.482500 PDF parameter B = 0.589300 X PDF CDF CDF_INV 0 0.482500 0.482500 1 2 0.125248 0.820285 3 0 0.482500 0.482500 1 1 0.212537 0.695037 2 0 0.482500 0.482500 1 0 0.482500 0.482500 1 3 0.738088E-01 0.894094 4 1 0.212537 0.695037 2 0 0.482500 0.482500 1 3 0.738088E-01 0.894094 4 QUASIGEOMETRIC_SAMPLE_test(): QUASIGEOMETRIC_mean() computes the Quasigeometric mean; QUASIGEOMETRIC_sample() samples the Quasigeometric distribution; QUASIGEOMETRIC_variance() computes the Quasigeometric variance. PDF parameter A = 0.482500 PDF parameter B = 0.589300 PDF mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.20100 Sample variance = 2.81141 Sample maximum = 13 Sample minimum = 0 R8_BETA_TEST: R8_BETA evaluates the Beta function. X Y BETA(X,Y) R8_BETA(X,Y) tabulated computed 0.200000 1.000000 5.000000000000000 4.999999999999998 0.400000 1.000000 2.500000000000000 2.500000000000000 0.600000 1.000000 1.666666666666667 1.666666666666667 0.800000 1.000000 1.250000000000000 1.250000000000000 1.000000 0.200000 5.000000000000000 4.999999999999998 1.000000 0.400000 2.500000000000000 2.500000000000000 1.000000 1.000000 1.000000000000000 1.000000000000000 2.000000 2.000000 0.1666666666666667 0.1666666666666667 3.000000 3.000000 0.3333333333333333E-01 0.3333333333333335E-01 4.000000 4.000000 0.7142857142857143E-02 0.7142857142857152E-02 5.000000 5.000000 0.1587301587301587E-02 0.1587301587301586E-02 6.000000 2.000000 0.2380952380952381E-01 0.2380952380952384E-01 6.000000 3.000000 0.5952380952380952E-02 0.5952380952380948E-02 6.000000 4.000000 0.1984126984126984E-02 0.1984126984126982E-02 6.000000 5.000000 0.7936507936507937E-03 0.7936507936507921E-03 6.000000 6.000000 0.3607503607503608E-03 0.3607503607503604E-03 7.000000 7.000000 0.8325008325008325E-04 0.8325008325008344E-04 R8_CEILING_test(): R8_CEILING rounds an R8 up. X R8_CEILING(X) -1.20000 -1 -1.00000 -1 -0.800000 0 -0.600000 0 -0.400000 0 -0.200000 0 0.00000 0 0.200000 1 0.400000 1 0.600000 1 0.800000 1 1.00000 1 1.20000 2 R8_ERROR_F_test(): R8_ERROR_F evaluates the error function erf(x). X -> Y = R8_ERROR_F(X) -> Z = R8_ERROR_F_INVERSE(Y) 0.260646 0.287581 0.260646 1.53121 0.969648 1.53121 -0.847230 -0.769147 -0.847230 0.559905 0.571537 0.559905 -1.81095 -0.989565 -1.81095 -0.998636E-01 -0.112311 -0.998636E-01 -1.52193 -0.968629 -1.52193 2.28123 0.998745 2.28123 0.106503 0.119723 0.106503 -0.973733 -0.831508 -0.973733 2.02546 0.995822 2.02546 -1.28177 -0.930122 -1.28177 -0.477272 -0.500301 -0.477272 0.202553 0.225469 0.202553 0.793860 0.738430 0.793860 -0.593572 -0.598776 -0.593572 0.169514 0.189459 0.169514 -1.62241 -0.978234 -1.62241 -0.374146E-01 -0.421981E-01 -0.374146E-01 0.229366 0.254344 0.229366 R8_FACTORIAL_test(): R8_FACTORIAL evaluates the factorial function. I R8_FACTORIAL(I) 0 1.00000 1 1.00000 2 2.00000 3 6.00000 4 24.0000 5 120.000 6 720.000 7 5040.00 8 40320.0 9 362880. 10 0.362880E+07 11 0.399168E+08 12 0.479002E+09 13 0.622702E+10 14 0.871783E+11 15 0.130767E+13 16 0.209228E+14 17 0.355687E+15 18 0.640237E+16 19 0.121645E+18 20 0.243290E+19 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) 0.1000 0.0300 0.738235 0.738235 0.1000 0.3000 0.908358 0.908358 0.1000 1.5000 0.988656 0.988656 0.5000 0.0750 0.301465 0.301465 0.5000 0.7500 0.779329 0.779329 0.5000 3.5000 0.991849 0.991849 1.0000 0.1000 0.951626E-01 0.951626E-01 1.0000 1.0000 0.632121 0.632121 1.0000 5.0000 0.993262 0.993262 1.1000 0.1000 0.720597E-01 0.720597E-01 1.1000 1.0000 0.589181 0.589181 1.1000 5.0000 0.991537 0.991537 2.0000 0.1500 0.101858E-01 0.101858E-01 2.0000 1.5000 0.442175 0.442175 2.0000 7.0000 0.992705 0.992705 6.0000 2.5000 0.420210E-01 0.420210E-01 6.0000 12.0000 0.979659 0.979659 11.0000 16.0000 0.922604 0.922604 26.0000 25.0000 0.447079 0.447079 41.0000 45.0000 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 0.00000 2 0.00000 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. 0.179769+309 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. 1.00000 19. 1.00000 20. 1.00000 21. 1.00000 22. 1.00000 23. 1.00000 24. 1.00000 25. 1.00000 3. 1.20206 3. 1.17905 3. 1.15915 3. 1.14185 4. 1.12673 4. 1.11347 4. 1.10179 4. 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 = 2.00000 X PDF CDF CDF_INV 0.887611 0.201091 0.937878E-01 0.887611 2.63801 0.276331 0.581002 2.63801 1.61373 0.291341 0.277844 1.61373 2.18522 0.300750 0.449483 2.18522 2.59633 0.279483 0.569419 2.59633 2.48323 0.287211 0.537359 2.48323 3.39934 0.200457 0.764122 3.39934 1.38665 0.272599 0.213647 1.38665 1.61608 0.291488 0.278530 1.61608 3.36367 0.204427 0.756901 3.36367 RAYLEIGH_SAMPLE_test(): RAYLEIGH_mean() computes the Rayleigh mean; RAYLEIGH_sample() samples the Rayleigh distribution; RAYLEIGH_variance() computes the Rayleigh variance. PDF parameter A = 2.00000 PDF mean = 2.50663 PDF variance = 1.71681 Sample size = 1000 Sample mean = 2.50564 Sample variance = 1.77092 Sample maximum = 7.89175 Sample minimum = 0.724486E-01 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 = 1.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 1.11354 0.817430 0.978891E-01 1.11354 1.87665 0.485034 0.572985 1.87665 2.71078 0.335785 0.907724 2.71078 2.39142 0.380627 0.793626 2.39142 1.72796 0.526772 0.497846 1.72796 1.44116 0.631602 0.332646 1.44116 1.45988 0.623502 0.344394 1.45988 1.02003 0.892369 0.180481E-01 1.02003 1.32197 0.688547 0.254069 1.32197 2.03946 0.446314 0.648713 2.03946 RECIPROCAL_SAMPLE_test(): RECIPROCAL_mean() computes the Reciprocal mean; RECIPROCAL_sample() samples the Reciprocal distribution; RECIPROCAL_variance() computes the Reciprocal variance. PDF parameter A = 1.00000 PDF parameter B = 3.00000 PDF mean = 1.82048 PDF variance = 0.326815 Sample size = 1000 Sample mean = 1.80556 Sample variance = 0.323281 Sample maximum = 2.99504 Sample minimum = 1.00002 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 1.00000 6 0 2 0.00000 6 1.00000 6 1 1 0.00000 6 1 2 0.285714 6 1 3 0.714286 6 1 4 0.00000 6 1.00000 6 2 1 0.00000 6 2 2 0.714286E-01 6 2 3 0.214286 6 2 4 0.357143 6 2 5 0.357143 6 2 6 0.00000 6 1.00000 6 3 1 0.00000 6 3 2 0.238095E-01 6 3 3 0.833333E-01 6 3 4 0.238095 6 3 5 0.297619 6 3 6 0.238095 6 3 7 0.119048 6 3 8 0.00000 6 1.00000 6 4 1 0.00000 6 4 2 0.952381E-02 6 4 3 0.380952E-01 6 4 4 0.142857 6 4 5 0.214286 6 4 6 0.285714 6 4 7 0.190476 6 4 8 0.952381E-01 6 4 9 0.238095E-01 6 4 10 0.00000 6 1.00000 6 5 1 0.00000 6 5 2 0.432900E-02 6 5 3 0.194805E-01 6 5 4 0.865801E-01 6 5 5 0.151515 6 5 6 0.259740 6 5 7 0.216450 6 5 8 0.173160 6 5 9 0.649351E-01 6 5 10 0.216450E-01 6 5 11 0.216450E-02 6 5 12 0.00000 6 1.00000 6 6 1 0.00000 6 6 2 0.216450E-02 6 6 3 0.108225E-01 6 6 4 0.541126E-01 6 6 5 0.108225 6 6 6 0.216450 6 6 7 0.216450 6 6 8 0.216450 6 6 9 0.108225 6 6 10 0.541126E-01 6 6 11 0.108225E-01 6 6 12 0.216450E-02 6 6 13 0.00000 6 6 14 0.00000 6 1.00000 6 7 1 0.00000 6 7 2 0.116550E-02 6 7 3 0.641026E-02 6 7 4 0.349650E-01 6 7 5 0.786713E-01 6 7 6 0.174825 6 7 7 0.203963 6 7 8 0.233100 6 7 9 0.145688 6 7 10 0.874126E-01 6 7 11 0.262238E-01 6 7 12 0.699301E-02 6 7 13 0.582751E-03 6 7 14 0.00000 6 1.00000 6 8 1 0.00000 6 8 2 0.666001E-03 6 8 3 0.399600E-02 6 8 4 0.233100E-01 6 8 5 0.582751E-01 6 8 6 0.139860 6 8 7 0.186480 6 8 8 0.233100 6 8 9 0.174825 6 8 10 0.116550 6 8 11 0.466200E-01 6 8 12 0.139860E-01 6 8 13 0.233100E-02 6 8 14 0.00000 6 1.00000 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 = 7.62000 Sample variance = 2.76436 Sample maximum = 11 Sample minimum = 2 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 = 3.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 2.00619 0.141343 0.347965 2.00619 4.96878 0.104369 0.772344 4.96878 1.42894 0.120142 0.272302 1.42894 10.4410 0.770560E-02 0.984583 10.4410 3.98699 0.141564 0.651071 3.98699 4.56514 0.120375 0.726986 4.56514 3.79951 0.147233 0.623987 3.79951 3.29345 0.157457 0.546537 3.29345 3.77074 0.148026 0.619739 3.77074 3.29921 0.157390 0.547444 3.29921 SECH_SAMPLE_test(): SECH_mean() computes the Sech mean; SECH_sample() samples the Sech distribution; SECH_variance() computes the Sech variance. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 3.00000 PDF variance = 9.86960 Sample size = 1000 Sample mean = 2.88805 Sample variance = 9.17117 Sample maximum = 21.8446 Sample minimum = -8.72738 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 = 3.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 2.36540 0.301861 0.301442 2.36523 1.50865 0.212093 0.739753E-01 1.50879 3.27667 0.315249 0.587786 3.27637 2.55560 0.310352 0.359715 2.55566 1.18299 0.133013 0.163810E-01 1.18359 2.14353 0.287647 0.235957 2.14355 1.31322 0.171027 0.363119E-01 1.31348 2.55501 0.310331 0.359532 2.55469 1.72156 0.244788 0.122784 1.72168 2.70916 0.314926 0.407750 2.70898 SEMICIRCULAR_SAMPLE_test(): SEMICIRCULAR_mean() computes the Semicircular mean; SEMICIRCULAR_sample() samples the Semicircular distribution; SEMICIRCULAR_variance() computes the Semicircular variance. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 3.00000 PDF variance = 1.00000 Sample size = 1000 Sample mean = 3.00698 Sample variance = 1.01773 Sample maximum = 4.97410 Sample minimum = 1.01699 STUDENT_CDF_test(): STUDENT_CDF evaluates the Student CDF. STUDENT_PDF evaluates the Student PDF. STUDENT_sample() samples the Student PDF. PDF parameter A = 0.500000 PDF parameter B = 2.00000 PDF parameter C = 6.00000 X PDF CDF -2.36431 0.566018E-01 0.101034 0.128815 0.368754 0.429440 5.08656 0.639873E-02 0.969167 -0.170357 0.339256 0.374449 0.334367 0.379901 0.468346 0.904916 0.366165 0.576875 1.19426 0.336329 0.629827 2.69161 0.116926 0.842406 0.915501 0.365310 0.578852 0.370527 0.381000 0.475243 STUDENT_SAMPLE_test(): STUDENT_mean() computes the Student mean; STUDENT_sample() samples the Student distribution; STUDENT_variance() computes the Student variance. PDF parameter A = 0.500000 PDF parameter B = 2.00000 PDF parameter C = 6.00000 PDF mean = 0.500000 PDF variance = 6.00000 Sample size = 1000 Sample mean = 0.522333 Sample variance = 2.02800 Sample maximum = 9.48864 Sample minimum = -8.72235 STUDENT_NONCENTRAL_CDF_test(): STUDENT_NONCENTRAL_CDF evaluates the Student Noncentral CDF; PDF argument X = 0.500000 PDF parameter IDF = 10 PDF parameter B = 1.00000 CDF value = 0.305280 TFN_test(): TFN evaluates Owen's T function; H A T(H,A) Exact 1.00000 0.500000 0.430647E-01 0.430647E-01 1.00000 1.00000 0.667419E-01 0.667419E-01 1.00000 2.00000 0.784682E-01 0.784682E-01 1.00000 3.00000 0.792995E-01 0.792995E-01 0.500000 0.500000 0.644886E-01 0.644886E-01 0.500000 1.00000 0.106671 0.106671 0.500000 2.00000 0.141581 0.141581 0.500000 3.00000 0.151084 0.151084 0.250000 0.500000 0.713466E-01 0.713466E-01 0.250000 1.00000 0.120129 0.120129 0.250000 2.00000 0.166613 0.166613 0.250000 3.00000 0.184750 0.184750 0.125000 0.500000 0.731727E-01 0.731727E-01 0.125000 1.00000 0.123763 0.123763 0.125000 2.00000 0.173744 0.173744 0.125000 3.00000 0.195119 0.195119 0.781250E-02 0.500000 0.737894E-01 0.737894E-01 0.781250E-02 1.00000 0.124995 0.124995 0.781250E-02 2.00000 0.176198 0.176198 0.781250E-02 3.00000 0.198777 0.198777 0.781250E-02 10.0000 0.234074 0.234089 0.781250E-02 100.000 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 = 1.00000 PDF parameter B = 3.00000 PDF parameter C = 10.0000 X PDF CDF CDF_INV 3.22572 0.215057 0.271573 3.22572 5.45874 0.144167 0.672651 5.45874 2.82911 0.203235 0.185870 2.82911 6.05379 0.125277 0.752816 6.05379 7.18382 0.894027E-01 0.874113 7.18382 2.83087 0.203430 0.186227 2.83087 3.99290 0.190702 0.427218 3.99290 4.19264 0.184360 0.464676 4.19264 7.16265 0.900745E-01 0.872214 7.16265 4.85415 0.163360 0.579686 4.85415 TRIANGLE_SAMPLE_test(): TRIANGLE_MEAN returns the Triangle mean; TRIANGLE_sample() samples the Triangle distribution; TRIANGLE_VARIANCE returns the Triangle variance; PDF parameter A = 1.00000 PDF parameter B = 3.00000 PDF parameter C = 10.0000 PDF parameter MEAN = 4.66667 PDF parameter VARIANCE = 3.72222 Sample size = 1000 Sample mean = 4.66586 Sample variance = 3.61019 Sample maximum = 9.93970 Sample minimum = 1.17781 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 = 1.00000 PDF parameter B = 10.0000 X PDF CDF CDF_INV 6.00998 0.197038 0.606908 6.00998 3.78779 0.137669 0.191896 3.78779 2.22365 0.604273E-01 0.369710E-01 2.22365 4.74829 0.185101 0.346906 4.74829 7.64096 0.116496 0.862591 7.64096 4.74348 0.184863 0.346016 4.74348 8.12452 0.926163E-01 0.913150 8.12452 9.22466 0.382882E-01 0.985157 9.22466 5.45521 0.220011 0.490097 5.45521 4.38273 0.167049 0.282540 4.38273 TRIANGULAR_SAMPLE_test(): TRIANGULAR_mean() computes the Triangular mean; TRIANGULAR_sample() samples the Triangular distribution; TRIANGULAR_variance() computes the Triangular variance. PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF mean = 5.50000 PDF variance = 3.37500 Sample size = 1000 Sample mean = 5.43551 Sample variance = 3.23113 Sample maximum = 9.59975 Sample minimum = 1.13031 UNIFORM_01_ORDER_SAMPLE_test(): UNIFORM_ORDER_sample() samples the Uniform 01 Order distribution. Ordered sample: 1 0.891951E-01 2 0.150959 3 0.316783 4 0.344358 5 0.549607 6 0.559286 7 0.601420 8 0.709423 9 0.841371 10 0.966220 UNIFORM_NSPHERE_SAMPLE_test(): UNIFORM_NSPHERE_sample() samples the Uniform Nsphere distribution. Dimension N of sphere = 3 Points on the sphere: 1 0.676488E-01 0.985270 -0.157055 2 0.841333 -0.434043 -0.322127 3 -0.162625 0.312239 0.935981 4 -0.234877 -0.971072 0.430338E-01 5 -0.953229 0.154106 0.260009 6 -0.127271 0.978010 0.165223 7 0.394715 0.670499 0.628197 8 0.102428 -0.487401 -0.867150 9 -0.896811 -0.342620 -0.279894 10 0.604658 0.566930 0.559446 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 0.535117 1.00000 0.535117 0.535117 0.235495 1.00000 0.235495 0.235495 0.274979 1.00000 0.274979 0.274979 0.527794 1.00000 0.527794 0.527794 0.983479 1.00000 0.983479 0.983479 0.240419 1.00000 0.240419 0.240419 0.408345 1.00000 0.408345 0.408345 0.865576E-01 1.00000 0.865576E-01 0.865576E-01 0.944350 1.00000 0.944350 0.944350 0.143484E-01 1.00000 0.143484E-01 0.143484E-01 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 = 0.500000 PDF variance = 0.833333E-01 Sample size = 1000 Sample mean = 0.515184 Sample variance = 0.823630E-01 Sample maximum = 0.999702 Sample minimum = 0.858449E-04 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 = 1.00000 PDF parameter B = 10.0000 X PDF CDF CDF_INV 5.22761 0.111111 0.469735 5.22761 9.16719 0.111111 0.907466 9.16719 1.45159 0.111111 0.501769E-01 1.45159 5.03267 0.111111 0.448075 5.03267 9.10032 0.111111 0.900035 9.10032 6.28455 0.111111 0.587173 6.28455 4.18233 0.111111 0.353592 4.18233 8.24014 0.111111 0.804460 8.24014 3.43264 0.111111 0.270293 3.43264 9.25647 0.111111 0.917385 9.25647 UNIFORM_SAMPLE_test(): UNIFORM_mean() computes the Uniform mean; UNIFORM_sample() samples the Uniform distribution; UNIFORM_variance() computes the Uniform variance. PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF mean = 5.50000 PDF variance = 6.75000 Sample size = 1000 Sample mean = 5.34084 Sample variance = 6.95972 Sample maximum = 9.97788 Sample minimum = 1.00584 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 3 0.166667 0.500000 4 4 0.166667 0.666667 5 5 0.166667 0.833333 6 6 0.166667 1.00000 6 3 0.166667 0.500000 4 6 0.166667 1.00000 6 6 0.166667 1.00000 6 4 0.166667 0.666667 5 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 = 3.50000 PDF variance = 2.91667 Sample size = 1000 Sample mean = 3.91900 Sample variance = 2.93137 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 = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 0.856447 0.505381 0.426448 0.856447 3.34429 0.172638E-01 0.990592 3.34431 -0.315834 0.115619 0.607065E-01 -0.315832 0.113869E-01 0.209680 0.112787 0.113853E-01 0.407434 0.366832 0.226122 0.407434 0.218641 0.288819 0.164241 0.218641 1.47739 0.412516 0.728965 1.47739 -0.541522E-01 0.187507 0.997803E-01 -0.541564E-01 4.13937 0.944882E-02 0.999979 4.13929 0.947641E-01 0.240059 0.131520 0.947656E-01 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 = 1.00000 PDF parameter B = 2.00000 PDF mean = 1.00000 PDF circular variance = 0.302225 Sample size = 1000 Sample mean = 1.01506 Sample circular variance = 0.306745 Sample maximum = 4.00947 Sample minimum = -1.96266 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 = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4.00000 X PDF CDF CDF_INV 6.15043 0.905421E-01 0.974355 6.15043 3.98794 0.319926 0.175362 3.98794 4.93652 0.499330 0.600687 4.93652 4.24826 0.409379 0.270524 4.24826 4.62767 0.497364 0.444878 4.62767 4.29967 0.425221 0.291979 4.29967 5.34784 0.392951 0.787934 5.34784 4.35076 0.440017 0.314090 4.35076 4.46682 0.469297 0.366921 4.46682 5.50787 0.328747 0.845774 5.50787 WEIBULL_SAMPLE_test(): WEIBULL_mean() computes the Weibull mean; WEIBULL_sample() samples the Weibull distribution; WEIBULL_variance() computes the Weibull variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4.00000 PDF mean = 4.71921 PDF variance = 0.581953 Sample size = 1000 Sample mean = 4.69360 Sample variance = 0.589554 Sample maximum = 7.07485 Sample minimum = 2.28352 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 = 0.500000 PDF parameter B = 1.50000 X PDF CDF CDF_INV 0 0.500000 0.500000 0 0 0.500000 0.500000 0 0 0.500000 0.500000 0 1 0.359214 0.859214 1 0 0.500000 0.500000 0 1 0.359214 0.859214 1 0 0.500000 0.500000 0 1 0.359214 0.859214 1 0 0.500000 0.500000 0 2 0.113508 0.972723 2 WEIBULL_DISCRETE_SAMPLE_test(): WEIBULL_DISCRETE_sample() samples the Weibull Discrete PDF. PDF parameter A = 0.500000 PDF parameter B = 1.50000 Sample size = 1000 Sample mean = 0.693000 Sample variance = 0.639390 Sample maximum = 4 Sample minimum = 0 ZIPF_CDF_test(): ZIPF_CDF evaluates the Zipf CDF. ZIPF_CDF_INV inverts the Zipf CDF. ZIPF_PDF evaluates the Zipf PDF. PDF parameter A = 2.00000 X PDF(X) CDF(X) CDF_INV(CDF) 1 0.607927 0.607927 1 2 0.151982 0.759909 2 3 0.675475E-01 0.827456 3 4 0.379954E-01 0.865452 4 5 0.243171E-01 0.889769 5 6 0.168869E-01 0.906656 6 7 0.124067E-01 0.919062 7 8 0.949886E-02 0.928561 8 9 0.750527E-02 0.936067 9 10 0.607927E-02 0.942146 10 11 0.502419E-02 0.947170 11 12 0.422172E-02 0.951392 12 13 0.359720E-02 0.954989 13 14 0.310167E-02 0.958091 14 15 0.270190E-02 0.960792 15 16 0.237472E-02 0.963167 16 17 0.210355E-02 0.965271 17 18 0.187632E-02 0.967147 18 19 0.168401E-02 0.968831 19 20 0.151982E-02 0.970351 20 ZIPF_SAMPLE_test(): ZIPF_mean() computes the mean of the Zipf distribution. ZIPF_sample() samples the Zipf distribution. ZIPF_variance() computes the variance of the Zipf distribution. PDF parameter A = 4.00000 PDF mean = 1.11063 PDF variance = 0.286326 Sample size = 1000 Sample mean = 1.10800 Sample variance = 0.202539 Sample maximum = 7 Sample minimum = 1 prob_test(): Normal end of execution. 6 October 2025 6:33:07.475 PM