14 November 2022 5:35:49.756 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 0.149348 0.883880 0.647137 0.149348 0.264485 0.967302 0.752322 0.264485 0.445877E-01 0.767270 0.544529 0.445877E-01 -0.527476E-01 0.628717 0.447350 -0.527476E-01 -0.477303 -0.168402 0.919569E-01 -0.477303 -0.285104 0.213532 0.230096 -0.285104 -0.527316E-02 0.699610 0.494727 -0.527316E-02 0.317400 0.988682 0.796508 0.317400 0.363827 0.998333 0.832560 0.363827 -0.557244 -0.323181 0.511574E-01 -0.557244 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 = -0.157035E-02 Sample variance = 0.114019 Sample maximum = 0.777231 Sample minimum = -0.766366 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 -0.384540 0.344824 0.374360 -0.384540 -0.331850 0.337431 0.392327 -0.331850 -0.997992 5.02589 0.201734E-01 -0.997992 -0.728605 0.464731 0.240169 -0.728605 0.998552 5.91721 0.982869 0.998552 0.804689 0.536149 0.797668 0.804689 0.582464 0.391594 0.697911 0.582464 0.830555 0.571538 0.811977 0.830555 -0.383776 0.344705 0.374624 -0.383776 0.830036 0.570745 0.811680 0.830036 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 = 0.120153E-01 Sample variance = 0.504149 Sample maximum = 0.999997 Sample minimum = -0.999999 PDF parameter A = 16.0000 PDF mean = 0.00000 PDF variance = 128.000 Sample size = 1000 Sample mean = -0.777192E-01 Sample variance = 130.088 Sample maximum = 16.0000 Sample minimum = -15.9999 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 1 0.301030 0.301030 1 9 0.457575E-01 1.00000 9 3 0.124939 0.602060 3 2 0.176091 0.477121 2 5 0.791812E-01 0.778151 5 4 0.969100E-01 0.698970 4 2 0.176091 0.477121 2 1 0.301030 0.301030 1 4 0.969100E-01 0.698970 4 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 = 3.50500 Sample variance = 5.98196 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 0 0.250000 0.250000 0 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 1 0.750000 1.00000 1 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 1 0.285714 0.500000 1 1 0.285714 0.500000 1 1 0.285714 0.500000 1 1 0.285714 0.500000 1 1 0.285714 0.500000 1 3 0.171429 0.928571 3 1 0.285714 0.500000 1 0 0.214286 0.214286 0 0 0.214286 0.214286 0 0 0.214286 0.214286 0 BETA_BINOMIAL_SAMPLE_test(): BETA_BINOMIAL_mean() computes the Beta Binomial mean; BETA_BINOMIAL_sample() samples the Beta Binomial distribution; BETA_BINOMIAL_variance() computes the Beta Binomial variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4 PDF mean = 1.60000 PDF variance = 1.44000 Sample size = 1000 Sample mean = 1.61400 Sample variance = 1.45446 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 0.367929 1.74587 0.961288E-01 0.367929 12.0000 12.0000 0.803094 0.250876E-01 0.999485 0.803094 12.0000 12.0000 0.484334 3.82676 0.439616 0.484334 12.0000 12.0000 0.536617 3.64614 0.638904 0.536617 12.0000 12.0000 0.525937 3.75536 0.599349 0.525937 12.0000 12.0000 0.423352 2.97797 0.227335 0.423352 12.0000 12.0000 0.393677 2.32524 0.148486 0.393677 12.0000 12.0000 0.573018 3.05167 0.761722 0.573018 12.0000 12.0000 0.502326 3.86741 0.508996 0.502326 12.0000 12.0000 0.553397 3.40977 0.698209 0.553397 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 = 0.405159 Sample variance = 0.398999E-01 Sample maximum = 0.942343 Sample minimum = 0.116630E-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 2 0.181147 0.235169 2 5 0.116029 1.00000 5 1 0.487703E-01 0.540225E-01 1 4 0.312386 0.883971 4 4 0.312386 0.883971 4 3 0.336416 0.571585 3 4 0.312386 0.883971 4 5 0.116029 1.00000 5 3 0.336416 0.571585 3 3 0.336416 0.571585 3 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 = 1.41400 Sample variance = 1.00761 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 0.217000E-01 0.223243E-01 11 0.260000E-01 0.241932E-01 12 0.230000E-01 0.258834E-01 13 0.285000E-01 0.273855E-01 14 0.280000E-01 0.286922E-01 15 0.316000E-01 0.297988E-01 16 0.301000E-01 0.307027E-01 17 0.307000E-01 0.314037E-01 18 0.358000E-01 0.319038E-01 19 0.309000E-01 0.322071E-01 20 0.304000E-01 0.323199E-01 21 0.324000E-01 0.322500E-01 22 0.336000E-01 0.320070E-01 23 0.308000E-01 0.316019E-01 24 0.323000E-01 0.310470E-01 25 0.287000E-01 0.303554E-01 26 0.300000E-01 0.295411E-01 27 0.282000E-01 0.286185E-01 28 0.275000E-01 0.276022E-01 29 0.278000E-01 0.265071E-01 30 0.245000E-01 0.253477E-01 31 0.253000E-01 0.241384E-01 32 0.233000E-01 0.228929E-01 33 0.208000E-01 0.216243E-01 34 0.214000E-01 0.203450E-01 35 0.204000E-01 0.190664E-01 36 0.166000E-01 0.177989E-01 37 0.173000E-01 0.165519E-01 38 0.151000E-01 0.153338E-01 39 0.159000E-01 0.141518E-01 40 0.131000E-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 1.48975 0.876395 0.652038 1.48975 1.40395 0.978386 0.572627 1.40395 1.47804 0.889045 0.641701 1.47804 1.05252 1.86947 0.105550 1.05252 1.20340 1.34395 0.343622 1.20340 1.70379 0.695529 0.818773 1.70379 1.64307 0.738783 0.775253 1.64307 1.23975 1.25871 0.390894 1.23975 1.02261 2.02659 0.473389E-01 1.02261 1.75951 0.660067 0.856522 1.75951 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 = 1.39011 Sample variance = 0.820834E-01 Sample maximum = 1.99978 Sample minimum = 1.00101 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 95 3.157895 0.163021E-01 10000 9553 3.140375 0.121790E-02 1000000 954566 3.142789 0.119684E-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 8 2.500000 0.641593 100 57 3.508772 0.367179 10000 6419 3.115750 0.258425E-01 1000000 637904 3.135268 0.632465E-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 3.00367 0.373282 0.751372 3.00367 2.36000 0.610836 0.421207 2.36000 1.82553 0.416850 0.127091 1.82553 2.70619 0.512720 0.619365 2.70619 1.81718 0.410888 0.123635 1.81718 4.24389 0.540179E-01 0.963951 4.24389 2.98454 0.382268 0.744147 2.98454 2.07213 0.560899 0.249148 2.07213 2.57864 0.563021 0.550636 2.57864 2.48382 0.591116 0.495844 2.48382 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 = 2.66364 Sample variance = 0.756705 Sample maximum = 9.36070 Sample minimum = 1.12061 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 0.871919 0.210352 0.699692 0.871919 0.967275 0.204319 0.719466 0.967275 3.10806 0.796222E-01 0.997331 3.10806 0.658764 0.222081 0.653558 0.658764 -0.973018 0.203942 0.279362 -0.973018 -0.672234 0.221419 0.343455 -0.672234 1.54276 0.161385 0.825085 1.54276 -0.284342 0.235537 0.432422 -0.284342 0.440986 0.231119 0.604151 0.440984 3.13554 0.795789E-01 0.999519 3.13554 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 = 0.790335E-01 Sample variance = 2.41092 Sample maximum = 3.13525 Sample minimum = -3.12905 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 0.939796 0.943231E-01 0.391870 0.939796 -9.44709 0.681918E-02 0.815863E-01 -9.44709 5.62486 0.431322E-01 0.779935 5.62486 4.12355 0.706860E-01 0.696071 4.12355 9.39965 0.149781E-01 0.877395 9.39965 4.12200 0.707204E-01 0.695961 4.12200 2.16950 0.105766 0.517965 2.16950 0.703549 0.894063E-01 0.370158 0.703549 4.47152 0.632051E-01 0.719350 4.47152 3.83706 0.771675E-01 0.674896 3.83706 CAUCHY_SAMPLE_test(): CAUCHY_mean() computes the Cauchy mean; CAUCHY_variance() computes the Cauchy variance; CAUCHY_sample() samples the Cauchy distribution. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 0.179769+309 Sample size = 1000 Sample mean = -2.18577 Sample variance = 22911.6 Sample maximum = 1256.46 Sample minimum = -3594.57 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 0.511055 0.370322 0.670745 0.511055 0.185413E-01 0.318365 0.505902 0.185413E-01 0.989043 2.15615 0.952836 0.989043 0.174491 0.323269 0.555828 0.174491 0.635824 0.412407 0.719340 0.635824 0.879952 0.670039 0.842426 0.879952 0.708315 0.450930 0.750544 0.708315 -0.840721 0.587865 0.182131 -0.840721 0.769636 0.498541 0.779562 0.769636 -0.893621 0.709210 0.148157 -0.893621 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 = 0.231030E-01 Sample variance = 0.479465 Sample maximum = 1.00000 Sample minimum = -0.999998 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 3.62843 0.290532 0.369087 3.62842 4.25548 0.281022 0.551128 4.25537 4.46441 0.267024 0.608458 4.46436 4.17880 0.284984 0.529424 4.17871 5.87375 0.121641 0.885352 5.87305 2.89339 0.228411 0.173664 2.89355 3.90904 0.293053 0.451242 3.90918 4.42719 0.269832 0.598465 4.42725 4.31605 0.277424 0.568043 4.31641 2.38035 0.149759 0.759431E-01 2.38086 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 = 4.24076 Sample variance = 1.89905 Sample maximum = 9.49516 Sample minimum = 1.25548 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 0.869700 0.140753 0.711330E-01 0.869700 4.44067 0.120534 0.650360 4.44067 5.67789 0.830213E-01 0.775470 5.67789 2.37486 0.181085 0.332825 2.37486 1.20785 0.165071 0.123196 1.20785 6.65212 0.597601E-01 0.844545 6.65212 1.17057 0.162987 0.117080 1.17057 4.97220 0.103464 0.709838 4.97220 1.96357 0.183909 0.257541 1.96357 3.66938 0.146466 0.547405 3.66938 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 = 9.85369 Sample variance = 18.6887 Sample maximum = 29.1123 Sample minimum = 1.36936 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 = 5.02013 Sample variance = 13.7516 Sample maximum = 20.8899 Sample minimum = 0.200660E-01 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 = -0.474053E-01 -0.280287E-01 Sample variance = 0.976416 0.953032 Sample maximum = 2.94548 2.93832 Sample minimum = -3.66325 -2.76235 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 = 0.991742 4.94930 Sample variance = 0.579429 0.566698 Sample maximum = 3.86780 7.86314 Sample minimum = -1.79529 2.44823 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 4.17672 -0.906420E-01 0.977257 4.17672 0.214446 -0.339176E-01 0.603215E-01 0.214446 3.56619 0.732419E-03 0.908421 3.56619 1.60960 0.147180 0.377299 1.60960 3.37598 0.308101E-01 0.875138 3.37598 1.52523 0.141552 0.351684 1.52523 -0.159845 -0.884217E-01 0.239175E-01 -0.159845 2.11351 0.158131 0.536094 2.11351 3.71806 -0.233529E-01 0.930870 3.71806 1.96318 0.159047 0.488283 1.96318 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 = 1.98113 Sample variance = 1.13786 Sample maximum = 4.77344 Sample minimum = -1.04342 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 16 2 5 3 9 4 12 5 23 6 14 7 8 8 6 9 10 10 9 Average wait was 11.2000 Number of coupon types is 10 Expected wait is about 23.0259 1 47 2 15 3 26 4 16 5 21 6 19 7 24 8 24 9 17 10 19 Average wait was 22.8000 Number of coupon types is 15 Expected wait is about 40.6208 1 50 2 79 3 46 4 38 5 55 6 55 7 30 8 46 9 91 10 38 Average wait was 52.8000 Number of coupon types is 20 Expected wait is about 59.9146 1 91 2 75 3 57 4 58 5 113 6 95 7 75 8 61 9 49 10 52 Average wait was 72.6000 Number of coupon types is 25 Expected wait is about 80.4719 1 82 2 79 3 84 4 136 5 111 6 61 7 100 8 176 9 145 10 110 Average wait was 108.400 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 0.113104 0.636383 0.571397 0.113037 0.619468 0.527209 0.819038 0.619629 0.142387 0.636035 0.589443 0.142334 -1.68273 0.271645E-01 0.308836E-01 -1.68359 -0.712376E-02 0.636620 0.495465 -0.708008E-02 -0.320227 0.623919 0.308902 -0.320312 -1.28181 0.154951 0.565130E-01 -1.28223 -0.494341 0.580895 0.227409 -0.494141 -2.98763 0.610637E-03 0.700275E-02 -2.98438 -0.564239 0.553054 0.200250 -0.564453 PDF parameter A = 0.785398 PDF parameter B = 0.500000 X PDF CDF CDF_INV -1.50979 0.997807E-01 0.161947 -1.51074 0.153135 0.318032 0.470614 0.153320 -5.77711 0.860010E-02 0.522429E-01 -5.78516 -0.798611 0.241723 0.236904 -0.798828 -6.29119 0.785392E-02 0.482153E-01 -6.29492 -1.41138 0.114253 0.169618 -1.41113 0.618461 0.278899 0.618746 0.618164 -4.25554 0.181255E-01 0.693018E-01 -4.25586 -0.770722 0.247947 0.241065 -0.770508 0.602780 0.281687 0.614301 0.602539 PDF parameter A = 1.57080 PDF parameter B = 0.00000 X PDF CDF CDF_INV 3.40928 0.252163E-01 0.909182 3.40918 0.515531 0.251475 0.651514 0.515625 -0.774537 0.198955 0.290227 -0.774414 -0.170912 0.309276 0.446118 -0.170898 -13.4455 0.175105E-02 0.236305E-01 -13.4766 -1.79637 0.753049E-01 0.161687 -1.79639 -0.408253 0.272836 0.376623 -0.408203 -0.174016 0.308954 0.445158 -0.173828 3.41673 0.251152E-01 0.909369 3.41406 -1.10578 0.143205 0.234024 -1.10645 DIPOLE_SAMPLE_test(): DIPOLE_sample() samples the Dipole distribution. PDF parameter A = 0.00000 PDF parameter B = 1.00000 Sample size = 10000 Sample mean = -0.454500E-04 Sample variance = 0.886542 Sample maximum = 12.1907 Sample minimum = -11.5268 PDF parameter A = 0.785398 PDF parameter B = 0.500000 Sample size = 10000 Sample mean = 0.999907 Sample variance = 14622.9 Sample maximum = 8264.19 Sample minimum = -6124.72 PDF parameter A = 1.57080 PDF parameter B = 0.00000 Sample size = 10000 Sample mean = -3.27093 Sample variance = 75170.6 Sample maximum = 978.840 Sample minimum = -26616.6 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 0.118825 0.355336E-01 0.939743 0.700621E-12 2 0.245919 0.616243E-01 0.993648 0.593495E-10 3 0.635257 0.771582E-01 0.999982 0.608567E-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 0.286821 0.565216E-01 0.931556 0.252647E-10 2 0.171358 0.401210E-01 0.973839 0.218640E-05 3 0.541821 0.671752E-01 0.999917 0.130834E-01 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 2 0.125000 0.187500 2 3 0.375000 0.562500 3 5 0.250000 0.937500 5 3 0.375000 0.562500 3 3 0.375000 0.562500 3 3 0.375000 0.562500 3 5 0.250000 0.937500 5 5 0.250000 0.937500 5 5 0.250000 0.937500 5 2 0.125000 0.187500 2 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 = 3.59300 Sample variance = 1.67703 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 = 9.98626 4.06315 Sample variance = 4.45390 Sample maximum = 12.9806 6.94759 Sample minimum = 7.04110 1.02645 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 0.00000 0.100000 0.100000 0.00000 1.00000 0.100000 0.200000 1.00000 2.00000 0.300000 0.500000 2.00000 0.00000 0.100000 0.100000 0.00000 4.50000 0.200000 0.700000 4.50000 2.00000 0.300000 0.500000 2.00000 1.00000 0.100000 0.200000 1.00000 2.00000 0.300000 0.500000 2.00000 1.00000 0.100000 0.200000 1.00000 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 = 4.29250 Sample variance = 11.3996 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 "i" 0.069660 0.466990 "i" "r" 0.059870 0.763220 "r" "c" 0.027820 0.124410 "c" "o" 0.075070 0.683110 "o" "a" 0.081670 0.081670 "a" "i" 0.069660 0.466990 "i" "u" 0.027580 0.944630 "u" "m" 0.024060 0.540550 "m" "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 43 0.478109E-02 0.957141 43 2 0.137319E-01 0.218106E-01 2 4 0.255292E-01 0.660031E-01 4 20 0.311022E-01 0.618405 20 9 0.329364E-01 0.232179 9 5 0.305008E-01 0.965039E-01 5 19 0.333674E-01 0.587303 19 19 0.333674E-01 0.587303 19 26 0.218306E-01 0.769034 26 3 0.186633E-01 0.404739E-01 3 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 = 19.2140 Sample variance = 155.476 Sample maximum = 74 Sample minimum = 1 ENGLISH_WORD_LENGTH_CDF_test(): ENGLISH_WORD_LENGTH_CDF evaluates the English Word Length CDF; ENGLISH_WORD_LENGTH_CDF_INV inverts the English Word Length CDF. ENGLISH_WORD_LENGTH_PDF evaluates the English Word Length PDF; X PDF CDF CDF_INV 4 0.156785 0.570067 4 4 0.156785 0.570067 4 5 0.108523 0.678590 5 4 0.156785 0.570067 4 11 0.158205E-01 0.981109 11 3 0.211926 0.413282 3 5 0.108523 0.678590 5 5 0.108523 0.678590 5 4 0.156785 0.570067 4 9 0.403212E-01 0.937628 9 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 = 4.61300 Sample variance = 6.79803 Sample maximum = 15 Sample minimum = 1 ERLANG_CDF_test(): ERLANG_CDF evaluates the Erlang CDF. ERLANG_CDF_INV inverts the Erlang CDF. ERLANG_PDF evaluates the Erlang PDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3 X PDF CDF CDF_INV 9.06953 0.207733 0.766946 9.07031 5.56307 0.383478 0.399059 5.56250 9.61302 0.180344 0.803461 9.61328 2.40143 0.175756 0.342284E-01 2.40234 6.34705 0.355808 0.499868 6.34766 9.76401 0.173145 0.812709 9.76562 6.79862 0.333871 0.553878 6.79883 6.13253 0.364949 0.473069 6.13281 2.70528 0.223553 0.552872E-01 2.70508 4.92452 0.390354 0.313109 4.92383 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 = 7.21733 Sample variance = 12.3429 Sample maximum = 27.2531 Sample minimum = 1.31241 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 5.22401 0.604974E-01 0.879005 5.22401 3.80012 0.123291 0.753418 3.80012 1.40400 0.408547 0.182906 1.40400 1.83458 0.329414 0.341171 1.83458 1.72285 0.348342 0.303316 1.72285 5.50940 0.524525E-01 0.895095 5.50940 2.43278 0.244257 0.511487 2.43278 1.67345 0.357053 0.285895 1.67345 1.05439 0.486585 0.268304E-01 1.05439 1.13887 0.466460 0.670802E-01 1.13887 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 = 10.9860 Sample variance = 108.736 Sample maximum = 98.8060 Sample minimum = 1.00417 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 0.167196 0.846034 0.153966 0.167196 0.417511 0.658684 0.341316 0.417511 0.477149 0.620550 0.379450 0.477149 0.868536 0.419565 0.580435 0.868536 0.937023 0.391792 0.608208 0.937023 0.654887 0.519501 0.480499 0.654887 2.52148 0.803407E-01 0.919659 2.52148 0.352954 0.702609 0.297391 0.352954 2.89444 0.553299E-01 0.944670 2.89444 0.383133 0.681722 0.318278 0.383133 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 = 0.980897 Sample variance = 0.897661 Sample maximum = 5.28593 Sample minimum = 0.628636E-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 0.931237 0.114140 0.239795 0.931237 -0.572106E-01 0.908896E-01 0.137348 -0.572106E-01 2.39018 0.121637 0.415596 2.39018 1.20454 0.117998 0.271544 1.20454 6.84348 0.543616E-01 0.819557 6.84348 2.23309 0.122266 0.396434 2.23309 -0.163340 0.876660E-01 0.127873 -0.163340 5.05630 0.838757E-01 0.696951 5.05630 -0.238955 0.853057E-01 0.121333 -0.238955 1.00153 0.115246 0.247857 1.00153 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 = 3.65300 Sample variance = 15.6663 Sample maximum = 32.0329 Sample minimum = -3.25798 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 9.47503 0.987199E-02 0.800029 0.239820E-01 2.00731 0.978108E-01 0.312301 0.434040 0.324424 4.27932 0.291464E-01 0.713340 0.221981 0.552876 0.280305 2.42351 0.597249E-01 0.636500 3.52319 0.374918E-01 0.688368 0.841865E-01 1.01187 0.179778 0.681451 0.229323 0.439330 0.992069 0.160426 0.498733 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 = 1.65822 Sample variance = 13.3715 Sample maximum = 87.8887 Sample minimum = 0.835800E-01 FERMI_DIRAC_SAMPLE_test(): FERMI_DIRAC_sample() samples the Fermi Dirac distribution. U = 1.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 0.604648 Sample variance = 0.178017 Maximum value = 2.66624 Minimum value = 0.107006E-03 U = 2.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 1.05111 Sample variance = 0.430313 Maximum value = 3.67525 Minimum value = 0.748903E-03 U = 4.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 2.02389 Sample variance = 1.44988 Maximum value = 5.60031 Minimum value = 0.278528E-04 U = 8.00000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 3.98622 Sample variance = 5.41124 Maximum value = 9.44406 Minimum value = 0.553251E-04 U = 16.0000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 8.01761 Sample variance = 21.4638 Maximum value = 17.3968 Minimum value = 0.446754E-02 U = 32.0000 V = 1.00000 SAMPLE_NUM = 10000 Sample mean = 15.9468 Sample variance = 85.8050 Maximum value = 32.7507 Minimum value = 0.215655E-02 U = 1.00000 V = 0.250000 SAMPLE_NUM = 10000 Sample mean = 0.510431 Sample variance = 0.905426E-01 Maximum value = 1.41090 Minimum value = 0.293622E-03 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 -0.1926 -0.4211 0.8863 0.795775E-01 0.6694 0.0260 0.7425 0.795775E-01 -0.0708 0.5419 0.8375 0.795775E-01 -0.9208 -0.0935 -0.3786 0.795775E-01 0.6371 0.2340 -0.7344 0.795775E-01 0.9410 -0.0625 0.3327 0.795775E-01 -0.9529 0.2084 0.2203 0.795775E-01 -0.8968 -0.0545 -0.4390 0.795775E-01 -0.1506 -0.3092 0.9390 0.795775E-01 0.9974 0.0256 -0.0672 0.795775E-01 PDF parameters: Concentration parameter KAPPA = 0.500000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF 0.7450 -0.5381 0.3941 0.110822 0.0445 -0.4179 0.9074 0.780755E-01 -0.3755 0.9219 -0.0956 0.632848E-01 -0.7161 -0.6729 -0.1856 0.533762E-01 0.1766 -0.9770 0.1199 0.834031E-01 -0.4085 0.8888 -0.2077 0.622487E-01 0.7819 -0.1545 0.6040 0.112883 -0.6273 0.7457 -0.2246 0.557984E-01 0.5421 0.1987 0.8164 0.100130 0.4428 0.8915 -0.0957 0.952780E-01 PDF parameters: Concentration parameter KAPPA = 10.0000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF 0.9505 0.0070 0.3107 0.970059 0.9396 -0.3363 0.0633 0.870080 0.9345 0.3492 -0.0694 0.826681 0.8681 -0.4818 -0.1194 0.425748 0.8803 -0.4510 -0.1468 0.481011 0.9076 0.2455 0.3407 0.631464 0.7483 -0.1406 -0.6483 0.128430 0.9591 -0.1264 -0.2534 1.05697 0.6774 -0.1688 -0.7160 0.632107E-01 0.9356 -0.3530 0.0026 0.836009 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 2.13517 0.345377 0.154583 2.13517 2.67742 0.417381 0.371060 2.67742 3.71277 0.225866 0.713914 3.71277 1.77551 0.201368 0.550892E-01 1.77551 2.50360 0.417556 0.298204 2.50360 2.32856 0.395834 0.226680 2.32856 1.75902 0.194226 0.518263E-01 1.75902 4.94317 0.776786E-01 0.884578 4.94317 8.28984 0.815804E-02 0.979767 8.28984 7.90711 0.100506E-01 0.976298 7.90711 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 = 3.56299 Sample variance = 4.07212 Sample maximum = 24.9804 Sample minimum = 1.23727 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 0.289895 0.212413 0.616842E-01 0.289919 1.59522 0.196628 0.330955 1.59513 3.14533 0.154185 0.605524 3.14512 2.49043 0.174595 0.497708 2.49024 3.32705 0.148073 0.632989 3.32740 2.82401 0.164560 0.554297 2.82411 4.25823 0.115267 0.755712 4.25740 2.40810 0.176937 0.483236 2.40786 0.442651 0.211680 0.940795E-01 0.442629 1.15248 0.204340 0.242108 1.15248 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 = 2.93353 Sample variance = 4.43735 Sample maximum = 13.7435 Sample minimum = 0.296448E-01 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 1.30459 0.660129 0.637386 1.30459 1.52043 0.422367 0.752383 1.52043 1.20195 0.808108 0.562203 1.20195 1.06609 1.01746 0.438101 1.06609 1.44165 0.497440 0.716231 1.44165 0.788607 1.00960 0.130158 0.788607 3.50117 0.195052E-01 0.976969 3.50117 1.25810 0.724713 0.605216 1.25810 1.84206 0.222037 0.852153 1.84206 0.994083 1.11003 0.361330 0.994083 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 = 1.38062 Sample variance = 0.889301 Sample maximum = 16.7089 Sample minimum = 0.538843 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 2.77877 0.143195 0.117458 4.93368 0.166486 0.487192 4.34208 0.178278 0.384798 4.39331 0.177615 0.393916 5.53806 0.148093 0.582470 5.44357 0.151222 0.568329 7.53667 0.810681E-01 0.809782 11.0681 0.182629E-01 0.963227 2.36196 0.110840 0.641760E-01 5.78382 0.139697 0.617841 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 = 6.98731 Sample variance = 17.3997 Sample maximum = 26.7311 Sample minimum = 1.06824 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 5.24791 0.114152 0.712624 5.24791 2.73558 0.154957 0.349339 2.73558 2.69795 0.154402 0.343518 2.69795 2.13569 0.141087 0.260019 2.13569 6.07776 0.873889E-01 0.796142 6.07776 3.23950 0.158177 0.428562 3.23950 7.60705 0.477184E-01 0.897374 7.60705 5.85010 0.945439E-01 0.775437 5.85010 4.87630 0.126097 0.667969 4.87630 2.95549 0.157322 0.383702 2.95549 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 = 4.05969 Sample variance = 8.10107 Sample maximum = 16.0716 Sample minimum = -3.61087 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 5 0.791016E-01 0.762695 6 1 0.250000 0.250000 2 6 0.593262E-01 0.822021 7 9 0.250282E-01 0.924915 10 7 0.444946E-01 0.866516 8 4 0.105469 0.683594 5 11 0.140784E-01 0.957765 12 5 0.791016E-01 0.762695 6 8 0.333710E-01 0.899887 9 14 0.593932E-02 0.982182 15 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 = 4.06300 Sample variance = 11.3524 Sample maximum = 23 Sample minimum = 1 GOMPERTZ_CDF_test(): GOMPERTZ_CDF evaluates the Gompertz CDF; GOMPERTZ_CDF_INV inverts the Gompertz CDF. GOMPERTZ_PDF evaluates the Gompertz PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 0.110551 2.29458 0.291562 0.110551 0.266071 1.50152 0.583787 0.266071 0.603756 0.480916 0.894513 0.603756 0.275225 1.46184 0.597351 0.275225 0.538677E-01 2.64136 0.151816 0.538677E-01 0.952136E-02 2.93455 0.282518E-01 0.952136E-02 0.839056 0.176553 0.967102 0.839056 0.626919 0.439350 0.905165 0.626919 0.141455 2.11869 0.359730 0.141455 0.814955E-01 2.46842 0.222385 0.814955E-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 = 0.276626 Sample variance = 0.551591E-01 Sample maximum = 1.46576 Sample minimum = 0.232461E-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 0.269029E-01 0.367748 0.377775 0.269029E-01 0.164066 0.363218 0.427977 0.164066 -1.03723 0.167937 0.595223E-01 -1.03723 -0.290265 0.351159 0.262690 -0.290265 0.137302 0.364580 0.418237 0.137302 -0.301078E-01 0.367711 0.356805 -0.301078E-01 1.12138 0.235225 0.721928 1.12138 -0.198496 0.360209 0.295358 -0.198496 -0.761585E-01 0.366787 0.339890 -0.761585E-01 1.77544 0.143009 0.844164 1.77544 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 = 0.574585 Sample variance = 1.50344 Sample maximum = 6.53713 Sample minimum = -1.94206 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 0.955415 0.355923 0.367142 0.955415 2.27188 0.209272 0.744019 2.27188 0.798734 0.368363 0.310377 0.798734 1.87819 0.256689 0.652319 1.87819 0.730384 0.373207 0.285032 0.730384 2.24458 0.212523 0.738260 2.24458 0.676442 0.376764 0.264803 0.676442 0.612169 0.380685 0.240460 0.612169 1.04578 0.347968 0.398948 1.04578 1.43549 0.308351 0.527084 1.43549 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 = 8.16358 Sample variance = 36.6015 Sample maximum = 35.0515 Sample minimum = 0.109086E-01 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 = 0.667000 Sample variance = 0.568680 Sample maximum = 4 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 1 197 2 21 3 76 4 -96 5 34 6 152 7 -59 8 26 9 97 10 10 11 169 12 121 13 177 14 30 15 -96 16 4 17 -88 18 85 19 5 20 -70 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 72 2 -100 3 0 4 -8 5 11 6 51 7 -60 8 93 9 99 10 190 11 181 12 -45 13 113 14 164 15 197 16 99 17 -16 18 124 19 98 20 95 I4VEC_UNIQUE_COUNT_test(): I4VEC_UNIQUE_COUNT counts unique entries in an I4VEC. Input vector: 1 14 2 13 3 11 4 0 5 20 6 11 7 14 8 12 9 16 10 4 11 4 12 11 13 1 14 5 15 0 16 13 17 20 18 9 19 1 20 5 Number of unique entries is 11 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 7.18758 0.285092E-01 0.812163 6.97101 0.299779E-01 0.805832 0.909397 0.311639 0.201147 1.03531 0.291789 0.239154 2.65497 0.120048 0.546636 3.72277 0.771815E-01 0.649412 2.18676 0.150956 0.483600 6.10907 0.370651E-01 0.777096 2.96668 0.104426 0.581536 2.14900 0.153945 0.477843 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 = 1.97894 Sample variance = 2.58326 Sample maximum = 13.0882 Sample minimum = 0.239756 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 -1.17568 0.842359E-01 0.168472 -1.17568 -0.439850 0.121697 0.243394 -0.439850 1.13591 0.233576 0.532848 1.13591 -2.72405 0.388395E-01 0.776789E-01 -2.72405 1.69476 0.176634 0.646732 1.69476 4.38174 0.460899E-01 0.907820 4.38174 0.179664 0.165885 0.331769 0.179664 1.97054 0.153883 0.692234 1.97054 6.67684 0.146295E-01 0.970741 6.67684 2.77598 0.102871 0.794259 2.77598 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 = 0.926042 Sample variance = 7.36805 Sample maximum = 13.2222 Sample minimum = -10.5614 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 2.24142 0.182268 0.204343 2.24142 8384.96 0.734851E-06 0.987677 8384.96 19890.6 0.201123E-06 0.991999 19890.6 1.74380 0.229274 0.101050 1.74380 5.83791 0.431191E-01 0.520248 5.83791 3.17511 0.111055 0.337608 3.17511 14.8745 0.101578E-01 0.704190 14.8745 1.74401 0.229264 0.101099 1.74401 18.8038 0.710007E-02 0.737501 18.8038 11.9325 0.142437E-01 0.668858 11.9325 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 1.13845 0.124850 0.517299 1.13845 -3.98183 0.353228E-01 0.764974E-01 -3.98183 0.167542 0.119739 0.397419 0.167542 -1.30690 0.911634E-01 0.239859 -1.30690 -4.57758 0.272884E-01 0.579330E-01 -4.57758 1.69534 0.121297 0.586053 1.69534 2.80302 0.102685 0.711260 2.80302 -0.137779 0.115408 0.361493 -0.137779 -2.90038 0.545122E-01 0.124533 -2.90038 -0.616148 0.106626 0.308301 -0.616148 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 = 1.69398 Sample variance = 30.7189 Sample maximum = 25.2123 Sample minimum = -29.0624 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 971797. 0.442625E-07 0.953819 971797. 7427.07 0.212431E-04 0.314490 7427.07 117.688 0.100892E-03 0.100275E-01 117.688 0.112122E+07 0.344015E-07 0.959650 0.112122E+07 197305. 0.558980E-06 0.835083 197305. 5880.85 0.253798E-04 0.278633 5880.85 449.713 0.883614E-04 0.418592E-01 449.713 47388.3 0.353086E-05 0.633261 47388.3 5888.94 0.253541E-04 0.278838 5888.94 16995.4 0.103636E-04 0.454126 16995.4 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 = 20.6194 Sample variance = 9187.36 Sample maximum = 1608.97 Sample minimum = 0.575794E-02 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 1 0.869015 0.869015 2 2 0.108627 0.977642 3 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 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 = 1.16000 Sample variance = 0.188589 Sample maximum = 5 Sample minimum = 1 LOG_UNIFORM_CDF_test(): LOG_UNIFORM_CDF evaluates the Log Uniform CDF; LOG_UNIFORM_CDF_INV inverts the Log Uniform CDF. LOG_UNIFORM_PDF evaluates the Log Uniform PDF; PDF parameter A = 2.00000 PDF parameter B = 20.0000 X PDF CDF CDF_INV 5.14855 0.843528E-01 0.410655 5.14855 5.09854 0.851802E-01 0.406416 5.09854 19.4466 0.223327E-01 0.987813 19.4466 16.7629 0.259081E-01 0.923319 16.7629 7.83013 0.554645E-01 0.592739 7.83013 9.44659 0.459737E-01 0.674245 9.44659 19.7902 0.219450E-01 0.995419 19.7902 4.95200 0.877008E-01 0.393751 4.95200 2.01791 0.215220 0.387263E-02 2.01791 2.40140 0.180851 0.794346E-01 2.40140 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 = 7.82362 Sample variance = 24.6478 Sample maximum = 19.9365 Sample minimum = 2.02429 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 -3.20802 0.281904E-01 0.961845E-01 -3.20802 -0.282485 0.294787 0.412365 -0.282485 9.24581 0.368052E-02 0.965706 9.24581 0.234415 0.301730 0.573293 0.234415 0.389500E-01 0.317828 0.512392 0.389500E-01 1.17359 0.133895 0.775367 1.17359 0.219538 0.303674 0.568790 0.219538 0.587710 0.236591 0.669129 0.587710 -0.368755 0.280207 0.387546 -0.368755 -0.725120E-01 0.316645 0.476959 -0.725120E-01 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 = -13.9016 Sample variance = 138745. Sample maximum = 458.324 Sample minimum = -11701.8 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 1.97766 0.239238 0.422944 1.97754 2.82926 0.293525 0.581295 2.82910 3.51799 0.262768 0.681563 3.51758 2.49756 0.285267 0.524268 2.49805 1.76023 0.209791 0.376374 1.76025 3.97683 0.218458 0.736024 3.97656 4.46939 0.164037 0.784963 4.46875 3.06428 0.289577 0.618179 3.06445 2.93749 0.292665 0.598636 2.93750 6.68925 0.166143E-01 0.917510 6.68750 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 = 3.12470 Sample variance = 1.85396 Sample maximum = 8.12756 Sample minimum = 0.292428 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 0.629000 0.571931 0 4 2 2.54400 1.24131 0 5 3 1.82700 1.17224 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 0.132921 2 0.764298E-01 3 0.452137 4 0.203831 5 0.134681 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 7 0.889893E-01 0.555054 7 13 0.316764E-01 0.873295 13 12 0.387155E-01 0.841618 12 7 0.889893E-01 0.555054 7 18 0.106490E-01 0.960536 18 11 0.469279E-01 0.802903 11 7 0.889893E-01 0.555054 7 3 0.937500E-01 0.156250 3 2 0.625000E-01 0.625000E-01 2 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 = 2.63400 Sample variance = 0.896941 Sample maximum = 9 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 0.2277420130626907 0.388729 0.590077 0.2277420130695196 -0.9429638841429850 0.255757 0.172850 -0.9429638841493184 0.2398146399759783 0.387634 0.594763 0.2398146399818715 -0.3810393524603344 0.371007 0.351587 -0.3810393524555039 2.084893269595859 0.453961E-01 0.981461 2.084893269584330 0.3521037501648777 0.374963 0.637620 0.3521037501614170 0.4983978406472626E-01 0.398447 0.519875 0.4983978406979598E-01 -0.3018650196488836 0.381174 0.381377 -0.3018650196492790 -1.595564048609078 0.111710 0.552931E-01 -1.595564048628106 0.8467012176714374 0.278764 0.801419 0.8467012176733741 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 = -0.149685E-01 Sample variance = 1.01284 Sample maximum = 3.41184 Sample minimum = -2.91072 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 112.092 0.192182E-01 0.789912 112.092 86.8281 0.180874E-01 0.189938 86.8281 97.1673 0.261261E-01 0.425106 97.1673 106.806 0.239948E-01 0.674984 106.806 89.2711 0.205934E-01 0.237225 89.2711 117.343 0.136317E-01 0.876195 117.343 104.997 0.251606E-01 0.630480 104.997 98.0755 0.263781E-01 0.448955 98.0755 104.992 0.251635E-01 0.630352 104.992 83.9483 0.150022E-01 0.142284 83.9483 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 = 100.187 Sample variance = 210.600 Sample maximum = 147.141 Sample minimum = 45.3439 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 93.9729 0.162395E-01 0.400204 93.9729 91.9276 0.158692E-01 0.367351 91.9276 143.506 0.367764E-02 0.980977 143.506 76.0125 0.105507E-01 0.152858 76.0125 67.7119 0.726081E-02 0.791104E-01 67.7119 85.3728 0.140883E-01 0.268721 85.3728 112.796 0.146659E-01 0.704940 112.796 101.273 0.166967E-01 0.521278 101.273 112.879 0.146408E-01 0.706161 112.879 124.689 0.102663E-01 0.854445 124.689 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 = 99.7357 Sample variance = 466.424 Sample maximum = 148.731 Sample minimum = 50.6085 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 95.5170 0.160687E-01 0.415546 95.5170 102.037 0.162751E-01 0.521584 102.037 117.681 0.127159E-01 0.754713 117.681 128.318 0.859718E-02 0.868337 128.318 125.489 0.971061E-02 0.842443 125.489 144.405 0.337202E-02 0.961269 144.405 106.383 0.158055E-01 0.591475 106.383 75.5701 0.101300E-01 0.144780 75.5701 79.6228 0.117138E-01 0.189062 79.6228 102.043 0.162748E-01 0.521682 102.043 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 = 100.901 Sample variance = 550.387 Sample maximum = 190.367 Sample minimum = 50.1373 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 123.064 0.106695E-01 0.841016 123.064 77.3304 0.108246E-01 0.186503 77.3304 131.504 0.738134E-02 0.917057 131.504 116.300 0.132023E-01 0.760095 116.300 87.1030 0.142947E-01 0.310023 87.1030 19.5016 0.915341E-04 0.656018E-03 19.5016 98.0612 0.162802E-01 0.480013 98.0612 128.146 0.866409E-02 0.890136 128.146 94.7056 0.159671E-01 0.425828 94.7056 75.3910 0.100591E-01 0.166252 75.3910 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 = 97.7278 Sample variance = 573.767 Sample maximum = 149.195 Sample minimum = 20.5236 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 0.504038 9.52886 0.394186E-01 0.504038 0.653936 1.99805 0.738680 0.653936 0.697903 1.35223 0.811255 0.697903 0.632140 2.44873 0.690412 0.632140 0.655004 1.97859 0.740803 0.655004 0.511653 8.70900 0.108803 0.511653 0.530110 7.04083 0.253517 0.530110 0.856392 0.396081 0.932160 0.856392 0.538801 6.38630 0.311811 0.538801 0.510719 8.80497 0.100627 0.510719 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 = 0.621196 Sample variance = 0.231552E-01 Sample maximum = 2.10575 Sample minimum = 0.500275 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 1.69061 0.419105 1.37986 0.437512 1.53268 0.433949 3.02159 0.161744 3.46683 0.100135 1.44384 0.437480 2.02801 0.362162 3.59585 0.863034E-01 1.10273 0.409174 2.99491 0.166153 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 = 1.91910 Sample variance = 1.00584 Sample maximum = 6.16554 Sample minimum = 0.148613 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 9 0.125110 0.457930 9 10 0.125110 0.583040 10 13 0.729079E-01 0.864464 13 12 0.947803E-01 0.791556 12 11 0.113736 0.696776 11 17 0.127640E-01 0.985722 17 7 0.900792E-01 0.220221 7 5 0.378333E-01 0.670860E-01 5 9 0.125110 0.457930 9 9 0.125110 0.457930 9 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 = 9.93300 Sample variance = 10.2468 Sample maximum = 23 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 2.35689 0.523753 0.617214 2.35689 2.86403 0.636451 0.911408 2.86403 2.16981 0.482179 0.523118 2.16981 2.69898 0.599773 0.809389 2.69898 2.91442 0.647649 0.943760 2.91442 0.420230 0.933844E-01 0.196215E-01 0.420230 2.95872 0.657493 0.972669 2.95872 2.02488 0.449974 0.455573 2.02488 2.43508 0.541128 0.658845 2.43508 1.16436 0.258747 0.150638 1.16436 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 = 2.01509 Sample variance = 0.470944 Sample maximum = 2.99742 Sample minimum = 0.948020E-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 0 0.482500 0.482500 1 1 0.212537 0.695037 2 4 0.434955E-01 0.937590 5 0 0.482500 0.482500 1 0 0.482500 0.482500 1 2 0.125248 0.820285 3 4 0.434955E-01 0.937590 5 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 = 1.27800 Sample variance = 3.39811 Sample maximum = 17 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) 0.988979E-01 0.111232 0.988979E-01 -0.962174 -0.826398 -0.962174 0.322002 0.351164 0.322002 -1.67714 -0.982300 -1.67714 0.491743 0.513214 0.491743 1.08496 0.875060 1.08496 0.253469 0.280001 0.253469 0.257149 0.283891 0.257149 0.779432 0.729661 0.779432 0.207891 0.231244 0.207891 -0.836024 -0.762920 -0.836024 1.02770 0.853883 1.02770 1.05600 0.864670 1.05600 -0.808704 -0.747244 -0.808704 1.77195 0.987787 1.77195 0.430656 0.457502 0.430656 -0.512016E-02 -0.577743E-02 -0.512016E-02 0.606512 0.608963 0.606512 -0.615835 -0.616204 -0.615835 1.71519 0.984719 1.71519 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. 0.100000E+31 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 3.85448 0.150441 0.843880 3.85448 2.03388 0.303179 0.403742 2.03388 1.13535 0.241597 0.148816 1.13535 3.00225 0.243261 0.675894 3.00225 6.10373 0.144895E-01 0.990504 6.10373 2.55358 0.282551 0.557404 2.55358 4.00828 0.134496 0.865782 4.00828 2.03796 0.303157 0.404981 2.03796 0.275046 0.681143E-01 0.941171E-02 0.275046 3.60274 0.177805 0.802589 3.60274 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 = 2.51200 Sample variance = 1.74424 Sample maximum = 8.21689 Sample minimum = 0.629214E-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 1.10524 0.823565 0.910836E-01 1.10524 1.68582 0.539939 0.475374 1.68582 1.48775 0.611824 0.361603 1.48775 2.27815 0.399553 0.749457 2.27815 1.17661 0.773610 0.148041 1.17661 1.65137 0.551202 0.456582 1.65137 1.35405 0.672232 0.275897 1.35405 1.44753 0.628821 0.336662 1.44753 1.61672 0.563014 0.437281 1.61672 1.90828 0.476995 0.588199 1.90828 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 = 1.81106 Sample variance = 0.325420 Sample maximum = 2.99774 Sample minimum = 1.00053 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 = 7.62900 Sample variance = 2.76412 Sample maximum = 11 Sample minimum = 3 SECH_CDF_test(): SECH_CDF evaluates the Sech CDF. SECH_CDF_INV inverts the Sech CDF. SECH_PDF evaluates the Sech PDF. PDF parameter A = 3.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV -0.934581 0.436573E-01 0.884483E-01 -0.934581 4.13369 0.136613 0.671480 4.13369 5.80004 0.739934E-01 0.846085 5.80004 2.27189 0.149161 0.386596 2.27189 6.70669 0.486874E-01 0.901039 6.70669 5.48717 0.847386E-01 0.821280 5.48717 -0.981896 0.426744E-01 0.864060E-01 -0.981896 -1.38601 0.350805E-01 0.707420E-01 -1.38601 3.15068 0.158704 0.523959 3.15068 1.12380 0.108030 0.237488 1.12380 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 = 2.89170 Sample variance = 9.57426 Sample maximum = 14.8768 Sample minimum = -11.5689 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 3.44978 0.310156 0.641954 3.44971 3.30429 0.314604 0.596483 3.30420 3.22433 0.316301 0.571256 3.22461 2.08086 0.282704 0.218081 2.08105 3.77479 0.293454 0.740308 3.77490 3.16846 0.317179 0.553558 3.16846 3.63441 0.301871 0.698500 3.63428 3.32389 0.314108 0.602646 3.32373 2.99754 0.318310 0.499218 2.99756 2.94590 0.318193 0.482782 2.94580 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 = 2.99727 Sample variance = 0.994761 Sample maximum = 4.99159 Sample minimum = 1.02175 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 -1.90963 0.935971E-01 0.136817 -0.212884 0.333998 0.366854 0.728285 0.377375 0.543576 1.19003 0.336852 0.629073 0.238868 0.375739 0.450193 -2.19607 0.685564E-01 0.113156 1.27458 0.325983 0.644046 0.298254E-01 0.360589 0.410979 -0.457095 0.300024 0.324600 -0.900346 0.229712 0.255021 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 = 0.541510 Sample variance = 3.61603 Sample maximum = 26.3754 Sample minimum = -17.0462 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 1.77926 0.865840E-01 0.337355E-01 1.77926 2.76330 0.195922 0.172734 2.76330 4.16357 0.185283 0.459304 4.16357 3.37757 0.210236 0.303863 3.37757 8.77774 0.388020E-01 0.976287 8.77774 7.14596 0.906044E-01 0.870706 7.14596 9.00404 0.316177E-01 0.984255 9.00404 2.16981 0.129979 0.760252E-01 2.16981 4.43798 0.176572 0.508951 4.43798 3.72471 0.199216 0.374932 3.72471 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 = 4.65686 Sample variance = 3.67827 Sample maximum = 9.59249 Sample minimum = 1.06123 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 2.71727 0.848035E-01 0.728153E-01 2.71727 7.82923 0.107199 0.883648 7.82923 5.73160 0.210785 0.550143 5.73160 7.18034 0.139242 0.803692 7.18034 8.95546 0.515821E-01 0.973060 8.95546 4.29078 0.162507 0.267388 4.29078 8.71437 0.634881E-01 0.959189 8.71437 6.38545 0.178496 0.677409 6.38545 2.61958 0.799793E-01 0.647664E-01 2.61958 5.00059 0.197560 0.395178 5.00059 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 = 5.58525 Sample variance = 3.29674 Sample maximum = 9.85428 Sample minimum = 1.27053 UNIFORM_01_ORDER_SAMPLE_test(): UNIFORM_ORDER_sample() samples the Uniform 01 Order distribution. Ordered sample: 1 0.154993E-01 2 0.198149 3 0.260738 4 0.426932 5 0.454888 6 0.636509 7 0.687533 8 0.764049 9 0.901642 10 0.971478 UNIFORM_NSPHERE_SAMPLE_test(): UNIFORM_NSPHERE_sample() samples the Uniform Nsphere distribution. Dimension N of sphere = 3 Points on the sphere: 1 -0.864575 0.322048 -0.385741 2 -0.849417 0.464901 0.249714 3 0.733455 0.669086 -0.119863 4 0.465774 -0.458998 0.756555 5 0.902530 -0.409583 -0.132969 6 -0.979904E-01 0.292339 0.951281 7 -0.170624 0.984247 0.463197E-01 8 0.229583 -0.721005 -0.653792 9 -0.779957 0.330676 -0.531339 10 0.335152 0.748011 0.572846 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 0.771181 1.00000 0.771181 0.771181 0.274180 1.00000 0.274180 0.274180 0.236284 1.00000 0.236284 0.236284 0.705135 1.00000 0.705135 0.705135 0.212267 1.00000 0.212267 0.212267 0.442556 1.00000 0.442556 0.442556 0.432256 1.00000 0.432256 0.432256 0.297021 1.00000 0.297021 0.297021 0.124595 1.00000 0.124595 0.124595 0.692036E-01 1.00000 0.692036E-01 0.692036E-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 = 0.503826 Sample variance = 0.833965E-01 Sample maximum = 0.999284 Sample minimum = 0.743393E-03 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 5.29592 0.111111 0.477324 5.29592 1.27159 0.111111 0.301767E-01 1.27159 9.80220 0.111111 0.978023 9.80220 1.39366 0.111111 0.437402E-01 1.39366 9.44152 0.111111 0.937947 9.44152 7.80262 0.111111 0.755846 7.80262 1.51140 0.111111 0.568219E-01 1.51140 5.72859 0.111111 0.525398 5.72859 3.72516 0.111111 0.302796 3.72516 3.90028 0.111111 0.322253 3.90028 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 = 5.52777 Sample variance = 6.61881 Sample maximum = 9.98929 Sample minimum = 1.00115 UNIFORM_DISCRETE_CDF_test(): UNIFORM_DISCRETE_CDF evaluates the Uniform Discrete CDF; UNIFORM_DISCRETE_CDF_INV inverts the Uniform Discrete CDF. UNIFORM_DISCRETE_PDF evaluates the Uniform Discrete PDF; PDF parameter A = 1 PDF parameter B = 6 X PDF CDF CDF_INV 6 0.166667 1.00000 6 5 0.166667 0.833333 6 3 0.166667 0.500000 4 5 0.166667 0.833333 6 6 0.166667 1.00000 6 6 0.166667 1.00000 6 4 0.166667 0.666667 5 3 0.166667 0.500000 4 5 0.166667 0.833333 6 5 0.166667 0.833333 6 UNIFORM_DISCRETE_SAMPLE_test(): UNIFORM_DISCRETE_mean() computes the Uniform Discrete mean; UNIFORM_DISCRETE_sample() samples the Uniform Discrete distribution; UNIFORM_DISCRETE_variance() computes the Uniform Discrete variance. PDF parameter A = 1 PDF parameter B = 6 PDF mean = 3.50000 PDF variance = 2.91667 Sample size = 1000 Sample mean = 3.89400 Sample variance = 2.90767 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 0.204735 0.283178 0.160264 0.204733 2.03277 0.194566 0.896135 2.03276 1.11428 0.509199 0.558698 1.11428 1.21909 0.491802 0.611246 1.21909 0.749671 0.484708 0.373498 0.749671 0.336243 0.337394 0.201052 0.336242 1.19518 0.496662 0.599430 1.19518 -0.414734 0.952727E-01 0.503069E-01 -0.414738 1.60977 0.359763 0.780127 1.60977 1.28859 0.474934 0.644864 1.28859 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 = 1.02909 Sample circular variance = 0.303824 Sample maximum = 3.99172 Sample minimum = -2.11220 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 3.73929 0.232073 0.106832 3.73929 3.27894 0.999505E-01 0.324914E-01 3.27894 4.21693 0.399320 0.257856 4.21693 4.17648 0.385946 0.241973 4.17648 5.27173 0.420307 0.756970 5.27173 4.02757 0.334106 0.188319 4.02757 5.27482 0.419251 0.758266 5.27482 4.91216 0.501880 0.588493 4.91216 3.28242 0.100731 0.328402E-01 3.28242 4.41370 0.456711 0.342318 4.41370 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 = 4.71426 Sample variance = 0.561797 Sample maximum = 7.02902 Sample minimum = 2.64205 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 1 0.359214 0.859214 1 0 0.500000 0.500000 0 0 0.500000 0.500000 0 0 0.500000 0.500000 0 2 0.113508 0.972723 2 0 0.500000 0.500000 0 0 0.500000 0.500000 0 0 0.500000 0.500000 0 1 0.359214 0.859214 1 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 = 0.663000 Sample variance = 0.608039 Sample maximum = 5 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 = 1.11800 Sample variance = 0.246322 Sample maximum = 9 Sample minimum = 1 prob_test(): Normal end of execution. 14 November 2022 5:35:50.579 PM