1 November 2024 2:58:02.590 PM prob_test(): Fortran77 version: Test prob(). TEST001 For the ANGLE PDF: ANGLE_CDF evaluates the CDF; PDF parameter N = 5 PDF argument X = 0.500000 CDF value = 0.107809E-01 TEST002 For the ANGLE PDF: ANGLE_PDF evaluates the PDF; PDF parameter N = 5 PDF argument X = 0.500000 PDF value = 0.826466E-01 TEST003 For the ANGLE PDF: ANGLE_MEAN computes the mean; PDF parameter N = 5 PDF mean = 1.57080 TEST004 For the Anglit PDF: ANGLIT_CDF evaluates the CDF; ANGLIT_CDF_INV inverts the CDF. ANGLIT_PDF evaluates the PDF; X PDF CDF CDF_INV -0.299105 0.186098 0.218418 -0.299105 0.574842 0.934378 0.956318 0.574842 0.359757 0.997830 0.829509 0.359757 0.618531E-01 0.788954 0.561695 0.618531E-01 -0.851032E-01 0.577115 0.415307 -0.851032E-01 -0.525341 -0.262184 0.661187E-01 -0.525341 -0.253093 0.275599 0.257578 -0.253093 -0.447402 -0.109188 0.109957 -0.447402 -0.574484 -0.355613 0.438290E-01 -0.574484 0.135623 0.870710 0.633966 0.135623 TEST005 For the Anglit PDF: ANGLIT_MEAN computes the mean; ANGLIT_SAMPLE samples; ANGLIT_VARIANCE computes the variance. PDF mean = 0.00000 PDF variance = 0.116850 Sample size = 1000 Sample mean = 0.239765E-02 Sample variance = 0.116844 Sample maximum = 0.739647 Sample minimum = -0.742509 TEST006 For the Arcsin PDF: ARCSIN_CDF evaluates the CDF; ARCSIN_CDF_INV inverts the CDF. ARCSIN_PDF evaluates the PDF; PDF parameter A = 1.00000 X PDF CDF CDF_INV -0.773671 0.502393 0.218418 -0.773671 0.990598 2.32679 0.956318 0.990598 0.859956 0.623687 0.829509 0.859956 0.192611 0.324384 0.561695 0.192611 -0.262942 0.329919 0.415307 -0.262942 -0.978504 1.54349 0.661187E-01 -0.978504 -0.690074 0.439813 0.257578 -0.690074 -0.940927 0.940048 0.109957 -0.940927 -0.990535 2.31906 0.438290E-01 -0.990535 0.408551 0.348743 0.633966 0.408551 TEST007 For the Arcsin PDF: ARCSIN_MEAN computes the mean; ARCSIN_SAMPLE samples; ARCSIN_VARIANCE computes the variance. PDF parameter A = 1.00000 PDF mean = 0.00000 PDF variance = 0.500000 Sample size = 1000 Sample mean = 0.986339E-02 Sample variance = 0.490326 Sample maximum = 0.999978 Sample minimum = -0.999983 PDF parameter A = 16.0000 PDF mean = 0.00000 PDF variance = 128.000 Sample size = 1000 Sample mean = -0.453245 Sample variance = 129.510 Sample maximum = 15.9995 Sample minimum = -15.9993 TEST008 For the Benford PDF: 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 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 TEST009 For the Bernoulli PDF, BERNOULLI_CDF evaluates the CDF; BERNOULLI_CDF_INV inverts the CDF. BERNOULLI_PDF evaluates the PDF; PDF parameter A = 0.750000 X PDF CDF CDF_INV 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 0 0.250000 0.250000 0 1 0.750000 1.00000 1 0 0.250000 0.250000 0 0 0.250000 0.250000 0 1 0.750000 1.00000 1 TEST010 For the Bernoulli PDF: BERNOULLI_MEAN computes the mean; BERNOULLI_SAMPLE samples; BERNOULLI_VARIANCE computes the variance. PDF parameter A = 0.750000 PDF mean = 0.750000 PDF variance = 0.187500 Sample size = 1000 Sample mean = 0.768000 Sample variance = 0.178354 Sample maximum = 1 Sample minimum = 0 TEST0105: BESSEL_I0 computes values of the Bessel I0 function. BESSEL_I0_VALUES returns some exact values. 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 TEST0106: BESSEL_I1 computes values of the Bessel I1 function. BESSEL_I1_VALUES returns some exact values. 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 TEST011 BETA evaluates the Beta function; GAMMA evaluates the Gamma function. Argument A = 2.20000 Argument B = 3.70000 Beta(A,B) = 0.453760E-01 (Expected value = 0.0454 ) Gamma(A)*Gamma(B)/Gamma(A+B) = 0.453760E-01 TEST012 For the Beta PDF: BETA_CDF evaluates the CDF; BETA_CDF_INV inverts the CDF. BETA_PDF evaluates the PDF; PDF parameter A = 12.0000 PDF parameter B = 12.0000 A B X PDF CDF CDF_INV 12.0000 12.0000 0.678986 0.855881 0.963719 0.678986 12.0000 12.0000 0.449603 3.45732 0.312092 0.449603 12.0000 12.0000 0.629299 1.80664 0.898948 0.629299 12.0000 12.0000 0.557035 3.34930 0.710504 0.557035 12.0000 12.0000 0.322395 0.877392 0.374775E-01 0.322395 12.0000 12.0000 0.301166 0.582322 0.221188E-01 0.301166 12.0000 12.0000 0.504229 3.86528 0.516356 0.504229 12.0000 12.0000 0.356011 1.49260 0.768453E-01 0.356011 12.0000 12.0000 0.470671 3.72441 0.387964 0.470671 12.0000 12.0000 0.539969 3.60494 0.651058 0.539969 TEST013: BETA_INC evaluates the normalized incomplete Beta function BETA_INC(A,B,X). BETA_INC_VALUES returns some exact values. 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 TEST014 For the Beta PDF: BETA_MEAN computes the mean; BETA_SAMPLE samples; BETA_VARIANCE computes the 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 = 0.403172 Sample variance = 0.407200E-01 Sample maximum = 0.940639 Sample minimum = 0.845055E-02 TEST015 For the Beta Binomial PDF, BETA_BINOMIAL_CDF evaluates the CDF; BETA_BINOMIAL_CDF_INV inverts the CDF. BETA_BINOMIAL_PDF evaluates the 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 4 0.714286E-01 1.00000 4 3 0.171429 0.928571 3 2 0.257143 0.757143 2 1 0.285714 0.500000 1 0 0.214286 0.214286 0 1 0.285714 0.500000 1 0 0.214286 0.214286 0 0 0.214286 0.214286 0 2 0.257143 0.757143 2 TEST016 For the Beta Binomial PDF: BETA_BINOMIAL_MEAN computes the mean; BETA_BINOMIAL_SAMPLE samples; BETA_BINOMIAL_VARIANCE computes the 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 = 1.62000 Sample variance = 1.40100 Sample maximum = 4 Sample minimum = 0 TEST020: BINOMIAL_CDF evaluates the cumulative distribution function for the discrete binomial probability density function. BINOMIAL_CDF_VALUES returns some exact values. A is the number of trials; B is the probability of success on one trial; X is the number of successes; BINOMIAL_CDF is the probability of having up to X successes. A B X Exact F BINOMIAL_CDF(A,B,X) 2 0.0500 0 0.902500 0.902500 2 0.0500 1 0.997500 0.997500 2 0.0500 2 1.00000 1.00000 2 0.5000 0 0.250000 0.250000 2 0.5000 1 0.750000 0.750000 4 0.2500 0 0.316406 0.316406 4 0.2500 1 0.738281 0.738281 4 0.2500 2 0.949219 0.949219 4 0.2500 3 0.996094 0.996094 10 0.0500 4 0.999936 0.999936 10 0.1000 4 0.998365 0.998365 10 0.1500 4 0.990126 0.990126 10 0.2000 4 0.967207 0.967207 10 0.2500 4 0.921873 0.921873 10 0.3000 4 0.849732 0.849732 10 0.4000 4 0.633103 0.633103 10 0.5000 4 0.376953 0.376953 TEST021 For the Binomial PDF: BINOMIAL_CDF evaluates the CDF; BINOMIAL_CDF_INV inverts the CDF. BINOMIAL_PDF evaluates the PDF; PDF parameter A = 5 PDF parameter B = 0.650000 X PDF CDF CDF_INV 3 0.336416 0.571585 3 5 0.116029 1.00000 5 3 0.336416 0.571585 3 4 0.312386 0.883971 4 3 0.336416 0.571585 3 3 0.336416 0.571585 3 2 0.181147 0.235169 2 4 0.312386 0.883971 4 5 0.116029 1.00000 5 2 0.181147 0.235169 2 TEST022 BINOMIAL_COEF evaluates binomial coefficients. BINOMIAL_COEF_LOG evaluates the logarithm. N K C(N,K) 0 0 1 1.00000 1 0 1 1.00000 1 1 1 1.00000 2 0 1 1.00000 2 1 2 2.00000 2 2 1 1.00000 3 0 1 1.00000 3 1 3 3.00000 3 2 3 3.00000 3 3 1 1.00000 4 0 1 1.00000 4 1 4 4.00000 4 2 6 6.00000 4 3 4 4.00000 4 4 1 1.00000 TEST023 For the Binomial PDF: BINOMIAL_MEAN computes the mean; BINOMIAL_SAMPLE samples; BINOMIAL_VARIANCE computes the variance. PDF parameter A = 5 PDF parameter B = 0.300000 PDF mean = 1.50000 PDF variance = 1.05000 Sample size = 1000 Sample mean = 1.52200 Sample variance = 1.02854 Sample maximum = 5 Sample minimum = 0 TEST0235 For the Birthday PDF, BIRTHDAY_CDF evaluates the CDF; BIRTHDAY_CDF_INV inverts the CDF. BIRTHDAY_PDF evaluates the PDF; N PDF CDF CDF_INV 1 0.00000 0.00000 0 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 TEST024 For the Bradford PDF: BRADFORD_CDF evaluates the CDF; BRADFORD_CDF_INV inverts the CDF. BRADFORD_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 1.11788 1.59869 0.218418 1.11788 1.92165 0.574785 0.956318 1.92165 1.71934 0.685254 0.829509 1.71934 1.39286 0.993325 0.561695 1.39286 1.25948 1.21682 0.415307 1.25948 1.03200 1.97451 0.661187E-01 1.03200 1.14305 1.51422 0.257578 1.14305 1.05489 1.85808 0.109957 1.05489 1.02088 2.03647 0.438290E-01 1.02088 1.46939 0.898629 0.633966 1.46939 TEST025 For the Bradford PDF: BRADFORD_MEAN computes the mean; BRADFORD_SAMPLE samples; BRADFORD_VARIANCE computes 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 = 1.39010 Sample variance = 0.795644E-01 Sample maximum = 1.99614 Sample minimum = 1.00085 TEST0251 BUFFON_LAPLACE_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 TEST0252 BUFFON_LAPLACE_SIMULATE simulates a Buffon-Laplace needle dropping experiment. On a grid of cells of width A and height B, a needle of length L is dropped at random. We count the number of times it crosses at least one grid line, and use this to estimate the value of PI. Cell width A = 1.000000 Cell height B = 1.000000 Needle length L = 1.000000 Trials Hits Est(Pi) Err 10 10 3.000000 0.141593 100 95 3.157895 0.163021E-01 10000 9571 3.134469 0.712395E-02 1000000 954905 3.141674 0.811255E-04 TEST0253 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 TEST0254 BUFFON_SIMULATE 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 64 3.125000 0.165927E-01 10000 6311 3.169070 0.274772E-01 1000000 636184 3.143745 0.215192E-02 TEST026 For the Burr PDF: BURR_CDF evaluates the CDF; BURR_CDF_INV inverts the CDF. BURR_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF parameter D = 2.00000 X PDF CDF CDF_INV 2.91469 0.364571 0.218418 2.91469 8.07561 0.179097E-01 0.956318 8.07561 5.33847 0.102359 0.829509 5.33847 3.88175 0.292999 0.561695 3.88175 3.43850 0.363335 0.415307 3.43850 2.40426 0.209864 0.661187E-01 2.40426 3.02016 0.376757 0.257578 3.02016 2.58327 0.278521 0.109957 2.58327 2.28429 0.161895 0.438290E-01 2.28429 4.15007 0.246070 0.633966 4.15007 TEST027 For the Burr PDF: BURR_MEAN computes the mean; BURR_VARIANCE computes the variance; BURR_SAMPLE samples; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF parameter D = 2.00000 PDF mean = 4.22453 PDF variance = 5.72505 Sample size = 1000 Sample mean = 4.21466 Sample variance = 4.28559 Sample maximum = 20.6931 Sample minimum = 1.71031 TEST0275 For the Cardioid PDF: CARDIOID_CDF evaluates the CDF; CARDIOID_CDF_INV inverts the CDF. CARDIOID_PDF evaluates the PDF; PDF parameter A = 0.00000 PDF parameter B = 0.250000 X PDF CDF CDF_INV -1.28896 0.181287 0.218419 -1.28895 2.61646 0.902998E-01 0.956317 2.61646 1.57037 0.159189 0.829509 1.57037 0.259396 0.236070 0.561695 0.259396 -0.357278 0.233707 0.415307 -0.357278 -2.38175 0.101466 0.661188E-01 -2.38175 -1.08178 0.196537 0.257578 -1.08178 -1.99504 0.126398 0.109957 -1.99504 -2.61484 0.903646E-01 0.438293E-01 -2.61484 0.571348 0.226093 0.633966 0.571348 TEST0276 For the Cardioid PDF: CARDIOID_MEAN computes the mean; CARDIOID_SAMPLE samples; CARDIOID_VARIANCE computes the variance. PDF parameter A = 0.00000 PDF parameter B = 0.250000 PDF mean = 0.00000 PDF variance = 0.00000 Sample size = 1000 Sample mean = 0.991354E-02 Sample variance = 2.28985 Sample maximum = 3.11531 Sample minimum = -3.11849 TEST028(): For the Cauchy PDF: cauchy_cdf() evaluates the CDF; cauchy_cdf_inv() inverts the CDF. cauchy_pdf() evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV -1.66329 0.425934E-01 0.218418 -1.66329 23.7233 0.198570E-02 0.956318 23.7233 7.05492 0.276373E-01 0.829509 7.05492 2.58886 0.102167 0.561695 2.58886 1.18240 0.987675E-01 0.415307 1.18240 -12.2343 0.451256E-02 0.661187E-01 -12.2343 -0.860458 0.555766E-01 0.257578 -0.860458 -6.33637 0.121655E-01 0.109957 -6.33637 -19.6498 0.199897E-02 0.438290E-01 -19.6498 3.34283 0.883932E-01 0.633966 3.34283 cauchy_sample_test(): cauchy_sample() samples. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = Infinite PDF mean = Infinite Sample size = 1000 Sample mean = 1.66442 Sample variance = 1579.41 Sample maximum = 458.532 Sample minimum = -517.438 TEST030 For the Chi PDF: CHI_CDF evaluates the CDF. CHI_CDF_INV inverts the CDF. CHI_PDF evaluates the PDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 4.66776 0.249667 0.661045 4.66797 3.69139 0.292127 0.387433 3.69141 5.68560 0.140774 0.860685 5.68555 7.01636 0.391311E-01 0.971355 7.01562 4.01933 0.290920 0.483460 4.01953 1.93024 0.774572E-01 0.250900E-01 1.92969 5.38454 0.173412 0.813437 5.38477 5.19739 0.194258 0.779034 5.19727 5.11671 0.203205 0.763000 5.11719 4.57428 0.258040 0.637312 4.57422 TEST031 For the Chi PDF: CHI_MEAN computes the mean; CHI_VARIANCE computes the variance; CHI_SAMPLE samples. 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 = 4.16297 Sample variance = 1.78593 Sample maximum = 8.34277 Sample minimum = 1.35360 TEST032: CHI_SQUARE_CDF evaluates the cumulative distribution function for the chi-square central probability density function. CHI_SQUARE_CDF_VALUES returns some exact values. A X Exact F CHI_SQUARE_CDF(A,X) 1 0.0100 0.796557E-01 0.796557E-01 2 0.0100 0.498752E-02 0.498752E-02 1 0.0200 0.112463 0.112463 2 0.0200 0.995017E-02 0.995017E-02 1 0.4000 0.472911 0.472911 2 0.4000 0.181269 0.181269 3 0.4000 0.597575E-01 0.597575E-01 4 0.4000 0.175231E-01 0.175231E-01 1 1.0000 0.682689 0.682689 2 1.0000 0.393469 0.393469 3 1.0000 0.198748 0.198748 4 1.0000 0.902040E-01 0.902040E-01 5 1.0000 0.374342E-01 0.374342E-01 3 2.0000 0.427593 0.427593 3 3.0000 0.608375 0.608375 3 4.0000 0.738536 0.738536 3 5.0000 0.828203 0.828203 3 6.0000 0.888390 0.888390 10 1.0000 0.172116E-03 0.172116E-03 10 2.0000 0.365985E-02 0.365985E-02 10 3.0000 0.185759E-01 0.185759E-01 TEST033 For the central chi square PDF: CHI_SQUARE_CDF evaluates the CDF; CHI_SQUARE_CDF_INV inverts the CDF. CHI_SQUARE_PDF evaluates the PDF; PDF parameter A = 4.00000 X PDF CDF CDF_INV 3.41653 0.154752 0.509317 3.41653 4.47034 0.119552 0.653921 4.47034 11.8250 0.799795E-02 0.981299 11.8250 2.27914 0.182306 0.315431 2.27914 4.93364 0.104660 0.705825 4.93364 4.49320 0.118798 0.656645 4.49320 7.04083 0.520795E-01 0.866254 7.04083 1.12602 0.160315 0.109878 1.12602 0.483101 0.948580E-01 0.248749E-01 0.483101 5.18019 0.971452E-01 0.730697 5.18019 TEST034 For the central chi square PDF: CHI_SQUARE_MEAN computes the mean; CHI_SQUARE_SAMPLE samples; CHI_SQUARE_VARIANCE computes the variance. PDF parameter A = 10.0000 PDF mean = 10.0000 PDF variance = 20.0000 Sample size = 1000 Sample mean = 10.0770 Sample variance = 20.2423 Sample maximum = 28.1620 Sample minimum = 1.20358 TEST035 For the noncentral chi square PDF: CHI_SQUARE_NONCENTRAL_SAMPLE samples. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 5.00000 PDF variance = 14.0000 Initial seed = 123456789 Final seed = 70876380 Sample size = 1000 Sample mean = 5.11159 Sample variance = 14.5293 Sample maximum = 21.9163 Sample minimum = 0.333674E-01 TEST036 CIRCLE_SAMPLE samples points in a circle. X coordinate of center is A = 10.0000 Y coordinate of center is B = 4.00000 Radius is C = 3.00000 Sample size = 1000 Sample mean = 9.99926 4.06034 Sample variance = 2.28924 2.19259 Sample maximum = 12.9218 6.96697 Sample minimum = 7.04381 1.03574 TEST037 For the Circular Normal 01 PDF: CIRCULAR_NORMAL_01_MEAN computes the mean; CIRCULAR_NORMAL_01_SAMPLE samples; CIRCULAR_NORMAL_01_VARIANCE computes variance. PDF means = 0.00000 0.00000 PDF variances = 1.00000 1.00000 Sample size = 1000 Sample mean = 0.581875E-02 0.215871E-01 Sample variance = 0.998375 1.00517 Sample maximum = 3.32858 3.02853 Sample minimum = -3.02975 -2.90483 TEST0375 For the Circular Normal PDF: CIRCULAR_NORMAL_MEAN computes the mean; CIRCULAR_NORMAL_SAMPLE samples; CIRCULAR_NORMAL_VARIANCE computes variance. PDF means = 1.00000 5.00000 PDF variances = 0.562500 0.562500 Sample size = 1000 Sample mean = 1.00436 5.01619 Sample variance = 0.561586 0.565407 Sample maximum = 3.49644 7.27140 Sample minimum = -1.27232 2.82138 TEST038 For the Cosine PDF: COSINE_CDF evaluates the CDF. COSINE_CDF_INV inverts the CDF. COSINE_PDF evaluates the PDF. PDF parameter A = 2.00000 PDF parameter B = 1.00000 X PDF CDF CDF_INV 1.04663 0.921411E-01 0.218496 1.04663 3.93128 -0.561385E-01 0.956298 3.93128 3.15509 0.642729E-01 0.829438 3.15509 2.19443 0.156156 0.561695 2.19443 1.73232 0.153487 0.415302 1.73232 0.258932 -0.269689E-01 0.660470E-01 0.258932 1.19619 0.110449 0.257478 1.19619 0.542718 0.180276E-01 0.109936 0.542718 0.702522E-01 -0.559100E-01 0.438598E-01 0.702522E-01 2.42721 0.144851 0.633937 2.42721 TEST039 For the Cosine PDF: COSINE_MEAN computes the mean; COSINE_SAMPLE samples; COSINE_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 1.00000 PDF mean = 2.00000 PDF variance = 1.28987 Sample size = 1000 Sample mean = 2.00654 Sample variance = 1.29547 Sample maximum = 4.71208 Sample minimum = -0.724350 TEST0395 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 TEST040 COUPON_SIMULATE simulates the coupon collector's problem. Number of coupon types is 5 Expected wait is about 8.04719 1 10 2 8 3 14 4 7 5 10 6 11 7 17 8 11 9 6 10 12 Average wait was 10.6000 Number of coupon types is 10 Expected wait is about 23.0259 1 29 2 31 3 47 4 42 5 27 6 31 7 44 8 23 9 11 10 30 Average wait was 31.5000 Number of coupon types is 15 Expected wait is about 40.6208 1 65 2 31 3 60 4 51 5 46 6 37 7 51 8 40 9 52 10 52 Average wait was 48.5000 Number of coupon types is 20 Expected wait is about 59.9146 1 80 2 80 3 51 4 54 5 58 6 80 7 173 8 69 9 156 10 54 Average wait was 85.5000 Number of coupon types is 25 Expected wait is about 80.4719 1 117 2 188 3 95 4 77 5 168 6 110 7 128 8 77 9 103 10 82 Average wait was 114.500 TEST041 For the Deranged PDF: DERANGED_CDF evaluates the CDF; DERANGED_CDF_INV inverts the CDF. DERANGED_PDF evaluates the PDF; PDF parameter A = 7 X PDF CDF CDF_INV 0 0.367857 0.367857 0 3 0.625000E-01 0.981746 3 2 0.183333 0.919246 2 1 0.368056 0.735913 1 1 0.368056 0.735913 1 0 0.367857 0.367857 0 0 0.367857 0.367857 0 0 0.367857 0.367857 0 0 0.367857 0.367857 0 1 0.368056 0.735913 1 TEST042 For the Deranged PDF: DERANGED_PDF evaluates the PDF. DERANGED_CDF evaluates the CDF. PDF parameter A = 7 X PDF(X) CDF(X) 0 0.367857 0.367857 1 0.368056 0.735913 2 0.183333 0.919246 3 0.625000E-01 0.981746 4 0.138889E-01 0.995635 5 0.416667E-02 0.999802 6 0.00000 0.999802 7 0.198413E-03 1.00000 TEST043 For the Deranged PDF: DERANGED_MEAN computes the mean. DERANGED_VARIANCE computes the variance. DERANGED_SAMPLE samples. PDF parameter A = 7 PDF mean = 1.00000 PDF variance = 0.632143 Sample size = 1000 Sample mean = 1.00400 Sample variance = 0.984969 Sample maximum = 5 Sample minimum = 0 TEST044: DIGAMMA evaluates the DIGAMMA or PSI function. PSI_VALUES returns some exact values. X Exact F DIGAMMA(X) 0.1000 -10.4238 -10.4238 0.2000 -5.28904 -5.28904 0.3000 -3.50252 -3.50252 0.4000 -2.56138 -2.56138 0.5000 -1.96351 -1.96351 0.6000 -1.54062 -1.54062 0.7000 -1.22002 -1.22002 0.8000 -0.965009 -0.965009 0.9000 -0.754927 -0.754927 1.0000 -0.577216 -0.577216 1.1000 -0.423755 -0.423755 1.2000 -0.289040 -0.289040 1.3000 -0.169191 -0.169191 1.4000 -0.613845E-01 -0.613845E-01 1.5000 0.364900E-01 0.364900E-01 1.6000 0.126047 0.126047 1.7000 0.208548 0.208548 1.8000 0.284991 0.284991 1.9000 0.356184 0.356184 2.0000 0.422784 0.422784 TEST045 For the Dipole PDF: DIPOLE_CDF evaluates the CDF. DIPOLE_CDF_INV inverts the CDF. DIPOLE_PDF evaluates the PDF. PDF parameter A = 0.00000 PDF parameter B = 1.00000 X PDF CDF CDF_INV 0.515107 0.573233 0.780988 0.515137 -1.28591 0.153127 0.561410E-01 -1.28516 0.467924 0.589867 0.761502 0.467773 0.295557 0.627128 0.677995 0.295410 -0.165270 0.635573 0.396656 -0.165283 -0.219095 0.633520 0.364799 -0.219238 0.507089E-01 0.636610 0.532227 0.507812E-01 0.883735 0.374656 0.888326 0.883789 -0.317761 0.624268 0.310195 -0.317871 0.298513 0.626776 0.679584 0.298340 PDF parameter A = 0.785398 PDF parameter B = 0.500000 X PDF CDF CDF_INV -2.00376 0.538127E-01 0.131477 -2.00293 1.90221 0.601880E-01 0.828708 1.90332 9.07094 0.368677E-02 0.964094 9.09375 0.244458 0.316631 0.501226 0.244629 0.203988 0.317466 0.487654 0.204102 -10.6175 0.288846E-02 0.291920E-01 -10.6211 -0.865020 0.226546 0.227479 -0.865234 2.15741 0.463925E-01 0.847767 2.15674 -4.81123 0.129237E-01 0.619356E-01 -4.81836 0.646407 0.273715 0.626535 0.646484 PDF parameter A = 1.57080 PDF parameter B = 0.00000 X PDF CDF CDF_INV -0.904508 0.175075 0.265947 -0.904297 -0.843581 0.185969 0.276943 -0.843750 0.227018 0.302709 0.571058 0.227051 -0.320266 0.288698 0.401342 -0.320312 -0.506838 0.253253 0.350680 -0.506836 0.251535 0.299369 0.578439 0.251465 -0.177728 0.308563 0.444012 -0.177734 -0.386329 0.276972 0.382650 -0.386230 -0.852594E-01 0.316013 0.472927 -0.849609E-01 -1.51135 0.969218E-01 0.186061 -1.51074 TEST046 For the Dipole PDF: DIPOLE_SAMPLE samples. PDF parameter A = 0.00000 PDF parameter B = 1.00000 Sample size = 1000 Sample mean = 0.171410E-01 Sample variance = 0.728062 Sample maximum = 4.78718 Sample minimum = -5.67547 PDF parameter A = 0.785398 PDF parameter B = 0.500000 Sample size = 1000 Sample mean = 0.283640 Sample variance = 252.082 Sample maximum = 245.982 Sample minimum = -245.584 PDF parameter A = 1.57080 PDF parameter B = 0.00000 Sample size = 1000 Sample mean = -0.179305 Sample variance = 242.215 Sample maximum = 119.648 Sample minimum = -335.780 TEST047 For the Dirichlet PDF: DIRICHLET_SAMPLE samples; DIRICHLET_MEAN computes the mean; DIRICHLET_VARIANCE computes the 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 0.132469 0.392217E-01 0.986951 0.118379E-10 2 0.240464 0.567061E-01 0.986585 0.198104E-05 3 0.627067 0.745858E-01 0.999945 0.490504E-02 TEST048 For the Dirichlet PDF: DIRICHLET_PDF evaluates the 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 TEST049 For the Dirichlet Mixture PDF: DIRICHLET_MIX_SAMPLE samples; DIRICHLET_MIX_MEAN computes the 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 2.00000 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 0.280835 0.578972E-01 0.915616 0.428373E-10 2 0.171392 0.361454E-01 0.924155 0.477996E-06 3 0.547774 0.603173E-01 0.999813 0.175771E-01 TEST050 For the Dirichlet mixture PDF: DIRICHLET_MIX_PDF evaluates the 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 2.00000 Component weights 1 1.00000 2 2.00000 PDF argument X: 1 0.500000 2 0.125000 3 0.375000 PDF value = 2.12288 TEST051 BETA_PDF evaluates the Beta PDF. DIRICHLET_PDF evaluates the Dirichlet PDF. For N = 2, Dirichlet = Beta. Number of components N = 2 PDF parameter A: 1 2.50000 2 3.50000 PDF argument X: 2.12288 Dirichlet PDF value = 1.65399 Beta PDF value = 1.65399 TEST052 For the Discrete PDF: DISCRETE_CDF evaluates the CDF; DISCRETE_CDF_INV inverts the CDF. DISCRETE_PDF evaluates the PDF; PDF parameter A = 6 PDF parameters B = 1 1.00000 2 2.00000 3 6.00000 4 2.00000 5 4.00000 6 1.00000 X PDF CDF CDF_INV 3 0.375000 0.562500 3 6 0.625000E-01 1.00000 6 5 0.250000 0.937500 5 3 0.375000 0.562500 3 3 0.375000 0.562500 3 2 0.125000 0.187500 2 3 0.375000 0.562500 3 2 0.125000 0.187500 2 1 0.625000E-01 0.625000E-01 1 4 0.125000 0.687500 4 TEST053 For the Discrete PDF: DISCRETE_MEAN computes the mean; DISCRETE_SAMPLE samples; DISCRETE_VARIANCE computes the 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 = 3.55900 Sample variance = 1.73826 Sample maximum = 6 Sample minimum = 1 TEST054 For the Empirical Discrete PDF: EMPIRICAL_DISCRETE_CDF evaluates the CDF; EMPIRICAL_DISCRETE_CDF_INV inverts the CDF. EMPIRICAL_DISCRETE_PDF evaluates the PDF; PDF parameter A = 6 PDF parameter B: 1 1.00000 2 1.00000 3 3.00000 4 2.00000 5 1.00000 6 2.00000 PDF parameter C: 1 0.00000 2 1.00000 3 2.00000 4 4.50000 5 6.00000 6 10.0000 X PDF CDF CDF_INV 2.00000 0.300000 0.500000 2.00000 10.0000 0.200000 1.00000 10.0000 10.0000 0.200000 1.00000 10.0000 4.50000 0.200000 0.700000 4.50000 2.00000 0.300000 0.500000 2.00000 0.00000 0.100000 0.100000 0.00000 2.00000 0.300000 0.500000 2.00000 1.00000 0.100000 0.200000 1.00000 0.00000 0.100000 0.100000 0.00000 4.50000 0.200000 0.700000 4.50000 TEST055 For the Empirical Discrete PDF: EMPIRICAL_DISCRETE_MEAN computes the mean; EMPIRICAL_DISCRETE_SAMPLE samples; EMPIRICAL_DISCRETE_VARIANCE computes the 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 = 4.23100 Sample variance = 11.2023 Sample maximum = 10.0000 Sample minimum = 0.00000 TEST056 For the Empirical Discrete PDF. EMPIRICAL_DISCRETE_PDF evaluates the PDF. EMPIRICAL_DISCRETE_CDF evaluates the CDF. 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(X) CDF(X) -2.0000 0.00000 0.00000 -1.0000 0.00000 0.00000 0.0000 0.100000 0.100000 1.0000 0.100000 0.200000 2.0000 0.300000 0.500000 3.0000 0.00000 0.500000 4.0000 0.00000 0.500000 5.0000 0.00000 0.700000 6.0000 0.100000 0.800000 7.0000 0.00000 0.800000 8.0000 0.00000 0.800000 9.0000 0.00000 0.800000 10.0000 0.200000 1.00000 11.0000 0.00000 1.00000 12.0000 0.00000 1.00000 TEST0563 For the English Sentence Length PDF: ENGLISH_SENTENCE_LENGTH_CDF evaluates the CDF; ENGLISH_SENTENCE_LENGTH_CDF_INV inverts the CDF. ENGLISH_SENTENCE_LENGTH_PDF evaluates the PDF; X PDF CDF CDF_INV 9 0.329364E-01 0.232179 9 43 0.478109E-02 0.957141 43 30 0.155962E-01 0.840951 30 19 0.333674E-01 0.587303 19 14 0.375972E-01 0.415634 14 5 0.305008E-01 0.965039E-01 5 10 0.354122E-01 0.267591 10 6 0.319642E-01 0.128468 6 4 0.255292E-01 0.660031E-01 4 21 0.287367E-01 0.647141 21 TEST0564 For the English Sentence Length PDF: ENGLISH_SENTENCE_LENGTH_MEAN computes the mean; ENGLISH_SENTENCE_LENGTH_SAMPLE samples; ENGLISH_SENTENCE_LENGTH_VARIANCE computes the variance. PDF mean = 19.1147 PDF variance = 147.443 Sample size = 1000 Sample mean = 19.1070 Sample variance = 144.238 Sample maximum = 67 Sample minimum = 1 TEST0565 For the English Word Length PDF: ENGLISH_WORD_LENGTH_CDF evaluates the CDF; ENGLISH_WORD_LENGTH_CDF_INV inverts the CDF. ENGLISH_WORD_LENGTH_PDF evaluates the PDF; X PDF CDF CDF_INV 3 0.212413 0.414231 3 10 0.277243E-01 0.967505 10 7 0.774196E-01 0.843006 7 4 0.157145 0.571376 4 4 0.157145 0.571376 4 2 0.170145 0.201818 2 3 0.212413 0.414231 3 2 0.170145 0.201818 2 2 0.170145 0.201818 2 5 0.108772 0.680148 5 TEST0566 For the English Word Length PDF: ENGLISH_WORD_LENGTH_MEAN computes the mean; ENGLISH_WORD_LENGTH_SAMPLE samples; ENGLISH_WORD_LENGTH_VARIANCE computes the variance. PDF mean = 4.75000 PDF variance = 7.07266 Sample size = 1000 Sample mean = 4.71700 Sample variance = 6.72163 Sample maximum = 14 Sample minimum = 1 TEST057 For the Erlang PDF: ERLANG_CDF evaluates the CDF. ERLANG_CDF_INV inverts the CDF. ERLANG_PDF evaluates the PDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3 X PDF CDF CDF_INV 11.2926 0.385403E-01 0.887143 11.2930 3.85983 0.122337 0.173777 3.85938 1.91828 0.332989E-01 0.114788E-01 1.91797 4.33148 0.131139 0.233762 4.33203 8.02827 0.919195E-01 0.681759 8.02734 6.42343 0.122108 0.509240 6.42383 5.14542 0.135161 0.342996 5.14551 4.95360 0.135317 0.317044 4.95312 6.71621 0.117176 0.544281 6.71680 5.95010 0.128886 0.449771 5.95020 TEST058 For the Erlang PDF: ERLANG_MEAN computes the mean; ERLANG_SAMPLE samples; ERLANG_VARIANCE computes the 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 = 7.00341 Sample variance = 11.4910 Sample maximum = 21.5166 Sample minimum = 1.22651 TEST059 ERROR_F evaluates the error function erf(x). ERROR_F_INVERSE inverts the error function. X -> Y = error_F(X) -> Z = error_f_inverse(Y) 1.67904 0.982428 1.67904 -0.472769 -0.496247 -0.472769 -0.566060 -0.576596 -0.566060 -0.231124 -0.256225 -0.231124 1.21293 0.913719 1.21293 0.535037 0.550744 0.535037 1.26938 0.927374 1.26938 1.04954 0.862265 1.04954 -1.66609 -0.981537 -1.66609 -1.86523 -0.991656 -1.86523 -2.24246 -0.998483 -2.24246 0.735809 0.701935 0.735809 0.396749E-01 0.447449E-01 0.396749E-01 -1.35074 -0.943896 -1.35074 0.673068 0.658833 0.673068 0.777484E-02 0.877279E-02 0.777484E-02 -0.275127 -0.302790 -0.275127 0.374940 0.404058 0.374940 2.16400 0.997789 2.16400 0.185600 0.207047 0.185600 TEST060 For the Exponential 01 PDF: EXPONENTIAL_01_CDF evaluates the CDF. EXPONENTIAL_01_CDF_INV inverts the CDF. EXPONENTIAL_01_PDF evaluates the PDF. X PDF CDF CDF_INV 0.246436 0.781582 0.218418 0.246436 3.13081 0.436824E-01 0.956318 3.13081 1.76907 0.170491 0.829509 1.76907 0.824841 0.438305 0.561695 0.824841 0.536668 0.584693 0.415307 0.536668 0.684060E-01 0.933881 0.661187E-01 0.684060E-01 0.297837 0.742422 0.257578 0.297837 0.116485 0.890043 0.109957 0.116485 0.448185E-01 0.956171 0.438290E-01 0.448185E-01 1.00503 0.366034 0.633966 1.00503 TEST061 For the Exponential 01_PDF: EXPONENTIAL_01_MEAN computes the mean; EXPONENTIAL_01_SAMPLE samples; EXPONENTIAL_01_VARIANCE computes the variance. PDF mean = 1.00000 PDF variance = 1.00000 Sample size = 1000 Sample mean = 1.00328 Sample variance = 0.981133 Sample maximum = 6.16979 Sample minimum = 0.184006E-02 TEST062 For the Exponential CDF: EXPONENTIAL_CDF evaluates the CDF. EXPONENTIAL_CDF_INV inverts the CDF. EXPONENTIAL_PDF evaluates the PDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 1.49287 0.390791 0.218418 1.49287 7.26162 0.218412E-01 0.956318 7.26162 4.53815 0.852454E-01 0.829509 4.53815 2.64968 0.219152 0.561695 2.64968 2.07334 0.292346 0.415307 2.07334 1.13681 0.466941 0.661187E-01 1.13681 1.59567 0.371211 0.257578 1.59567 1.23297 0.445022 0.109957 1.23297 1.08964 0.478086 0.438290E-01 1.08964 3.01006 0.183017 0.633966 3.01006 TEST063 For the Exponential PDF: EXPONENTIAL_MEAN computes the mean; EXPONENTIAL_SAMPLE samples; EXPONENTIAL_VARIANCE computes the variance. PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF mean = 11.0000 PDF variance = 100.000 Sample size = 1000 Sample mean = 11.0328 Sample variance = 98.1133 Sample maximum = 62.6979 Sample minimum = 1.01840 TEST064 For the Extreme Values CDF: EXTREME_VALUES_CDF evaluates the CDF; EXTREME_VALUES_CDF_INV inverts the CDF. EXTREME_VALUES_PDF evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 0.741219 0.110763 0.218418 0.741219 11.3257 0.142380E-01 0.956318 11.3257 7.03121 0.516842E-01 0.829509 7.03121 3.65080 0.107994 0.561695 3.65080 2.38781 0.121649 0.415307 2.38781 -0.997815 0.598662E-01 0.661187E-01 -0.997815 1.08542 0.116462 0.257578 1.08542 -0.375810 0.809160E-01 0.109957 -0.375810 -1.42066 0.456911E-01 0.438290E-01 -1.42066 4.35736 0.963122E-01 0.633966 4.35736 TEST065 For the Extreme Values PDF: EXTREME_VALUES_MEAN computes the mean; EXTREME_VALUES_SAMPLE samples; EXTREME_VALUES_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 3.73165 PDF variance = 14.8044 Sample size = 1000 Sample mean = 3.74498 Sample variance = 14.6723 Sample maximum = 20.5062 Sample minimum = -3.52111 TEST066: F_CDF evaluates the F central CDF. F_CDF_VALUES returns some exact values. A B X Exact F F_CDF(A,B,X) 1 1 1.0000 0.500000 0.500000 1 5 0.5280 0.499971 0.499971 5 1 1.8900 0.499603 0.499603 1 5 1.6900 0.749699 0.749699 2 10 1.6000 0.750466 0.750466 4 20 1.4700 0.751416 0.751416 1 5 4.0600 0.899987 0.899987 6 6 3.0500 0.899713 0.899713 8 16 2.0900 0.900285 0.900285 1 5 6.6100 0.950025 0.950025 3 10 3.7100 0.950057 0.950057 6 12 3.0000 0.950193 0.950193 1 5 10.0100 0.975013 0.975013 1 5 16.2600 0.990002 0.990002 1 5 22.7800 0.994998 0.994998 1 5 47.1800 0.999000 0.999000 2 5 1.0000 0.568799 0.568799 3 5 1.0000 0.535145 0.535145 4 5 1.0000 0.514343 0.514343 5 5 1.0000 0.500000 0.500000 TEST067 For the central F PDF: F_CDF evaluates the CDF. F_PDF evaluates the PDF. F_SAMPLE samples the PDF. PDF parameter M = 1 PDF parameter N = 1 X PDF CDF 12.6132 0.658382E-02 0.825270 5.99838 0.185710E-01 0.753218 5.13933 0.228705E-01 0.735525 1.46280 0.106864 0.560173 0.797869 0.198210 0.464137 9.28796 0.101522E-01 0.798156 0.862763E-03 10.8275 0.186939E-01 7494.37 0.490557E-06 0.992647 0.538447 0.281965 0.403009 135.944 0.199354E-03 0.945532 TEST068 For the central F PDF: F_MEAN computes the mean; F_SAMPLE samples; F_VARIANCE computes the varianc. PDF parameter M = 8 PDF parameter N = 6 PDF mean = 1.50000 PDF variance = 3.37500 Sample size = 1000 Sample mean = 1.44760 Sample variance = 3.10414 Sample maximum = 27.6769 Sample minimum = 0.641745E-01 TEST069 FACTORIAL_LOG evaluates the log of the factorial function; GAMMA_LOG_INT evaluates the log for integer argument. I GAMMA_LOG_INT(I+1) FACTORIAL_LOG(I) 1 0.00000 0.00000 2 0.693147 0.693147 3 1.79176 1.79176 4 3.17805 3.17805 5 4.78749 4.78749 6 6.57925 6.57925 7 8.52516 8.52516 8 10.6046 10.6046 9 12.8018 12.8018 10 15.1044 15.1044 11 17.5023 17.5023 12 19.9872 19.9872 13 22.5522 22.5522 14 25.1912 25.1912 15 27.8993 27.8993 16 30.6719 30.6719 17 33.5051 33.5051 18 36.3954 36.3954 19 39.3399 39.3399 20 42.3356 42.3356 TEST070 FACTORIAL_STIRLING computes Stirling's approximate factorial function; I4_FACTORIAL evaluates the factorial function; N Stirling N! 0 1.00000 1 1 1.00227 1 2 2.00065 2 3 6.00060 6 4 24.0010 24 5 120.003 120 6 720.009 720 7 5040.04 5040 8 40320.2 40320 9 362881. 362880 10 0.362881E+07 3628800 11 0.399169E+08 39916800 12 0.479002E+09 479001600 13 0.622703E+10 1932053504 TEST07025 Test FERMI_DIRAC_SAMPLE: U = 1.00000 V = 1.00000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.188319E-02 Maximum value = 2.16593 Sample mean = 0.601613 Sample variance = 0.175050 U = 2.00000 V = 1.00000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.367819E-02 Maximum value = 3.00626 Sample mean = 1.05710 Sample variance = 0.427542 U = 4.00000 V = 1.00000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.735349E-02 Maximum value = 4.83804 Sample mean = 2.03774 Sample variance = 1.41783 U = 8.00000 V = 1.00000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.147070E-01 Maximum value = 8.66413 Sample mean = 4.03715 Sample variance = 5.37055 U = 16.0000 V = 1.00000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.294139E-01 Maximum value = 16.4843 Sample mean = 8.05498 Sample variance = 21.1771 U = 32.0000 V = 1.00000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.588279E-01 Maximum value = 32.2945 Sample mean = 16.1002 Sample variance = 84.4008 U = 1.00000 V = 0.250000 SAMPLE_NUM = 1000 SEED = 123456789 Minimum value = 0.183837E-02 Maximum value = 1.20951 Sample mean = 0.509434 Sample variance = 0.886142E-01 TEST0705 For the Fisher PDF: FISHER_SAMPLE samples the PDF. FISHER_PDF evaluates the PDF. PDF parameters: Concentration parameter KAPPA = 0.00000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF -0.5632 0.3125 -0.7650 0.795775E-01 0.9126 0.1274 0.3884 0.795775E-01 0.6590 0.4371 0.6121 0.795775E-01 0.1234 -0.9919 -0.0291 0.795775E-01 -0.1694 -0.9424 -0.2885 0.795775E-01 -0.8678 0.0057 -0.4969 0.795775E-01 -0.4848 -0.5251 -0.6994 0.795775E-01 -0.7801 0.5044 0.3701 0.795775E-01 -0.9123 0.2292 -0.3393 0.795775E-01 0.2679 0.0823 -0.9599 0.795775E-01 PDF parameters: Concentration parameter KAPPA = 0.500000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF -0.3627 0.3524 -0.8627 0.636934E-01 0.9440 0.1029 0.3135 0.122414 0.7719 0.3694 0.5173 0.112322 0.3511 -0.9359 -0.0275 0.910105E-01 0.0772 -0.9533 -0.2919 0.793613E-01 -0.7848 0.0072 -0.6197 0.515738E-01 -0.2671 -0.5786 -0.7706 0.668096E-01 -0.6539 0.6100 0.4476 0.550623E-01 -0.8548 0.2905 -0.4301 0.498000E-01 0.4737 0.0753 -0.8775 0.967616E-01 PDF parameters: Concentration parameter KAPPA = 10.0000 Direction MU(1:3) = 1.0000 0.0000 0.0000 X PDF 0.8479 0.2005 -0.4908 0.347624 0.9955 0.0294 0.0897 1.52203 0.9813 0.1118 0.1566 1.32020 0.9423 -0.3346 -0.0098 0.893966 0.9121 -0.3919 -0.1200 0.660982 0.7284 0.0079 -0.6851 0.105231 0.8644 -0.3019 -0.4022 0.409948 0.7792 0.5053 0.3708 0.175002 0.6873 0.4066 -0.6020 0.697560E-01 0.9544 0.0255 -0.2974 1.00899 TEST071 For the Fisk PDF: FISK_CDF evaluates the CDF; FISK_CDF_INV inverts the CDF. FISK_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 2.30758 0.391667 0.218418 2.30758 6.59494 0.223993E-01 0.956318 6.59494 4.38899 0.125191 0.829509 4.38899 3.17239 0.339985 0.561695 3.17239 2.78448 0.408233 0.415307 2.78448 1.82738 0.223887 0.661187E-01 1.82738 2.40534 0.408224 0.257578 2.40534 1.99609 0.294750 0.109957 1.99609 1.71577 0.175649 0.438290E-01 1.71577 3.40184 0.289844 0.633966 3.40184 TEST072 For the Fisk PDF: FISK_MEAN computes the mean; FISK_SAMPLE samples; FISK_VARIANCE computes the 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 = 3.41120 Sample variance = 2.91484 Sample maximum = 16.6277 Sample minimum = 1.24516 TEST073 For the Folded Normal PDF: FOLDED_NORMAL_CDF evaluates the CDF. FOLDED_NORMAL_CDF_INV inverts the CDF. FOLDED_NORMAL_PDF evaluates the PDF. PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 1.03703 0.205965 0.218421 1.03703 7.16445 0.314698E-01 0.956292 7.16364 4.97681 0.901798E-01 0.829447 4.97609 2.86891 0.163148 0.561656 2.86863 2.03443 0.186808 0.415234 2.03394 0.310759 0.212331 0.661153E-01 0.310758 1.22833 0.203183 0.257565 1.22824 0.517615 0.211208 0.109931 0.517593 0.206128 0.212686 0.438790E-01 0.206146 3.33313 0.147866 0.633889 3.33255 TEST074 For the Folded Normal PDF: FOLDED_NORMAL_MEAN computes the mean; FOLDED_NORMAL_SAMPLE samples; FOLDED_NORMAL_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.90672 PDF variance = 4.55099 Sample size = 1000 Sample mean = 2.92096 Sample variance = 4.50179 Sample maximum = 10.6319 Sample minimum = 0.881944E-02 TEST0744 For the Frechet PDF: FRECHET_CDF evaluates the CDF; FRECHET_CDF_INV inverts the CDF. FRECHET_PDF evaluates the PDF; PDF parameter ALPHA = 3.00000 X PDF CDF CDF_INV 0.869476 1.14652 0.218418 0.869476 2.81845 0.454656E-01 0.956318 2.81845 1.74896 0.265962 0.829509 1.74896 1.20132 0.809067 0.561695 1.20132 1.04403 1.04866 0.415307 1.04403 0.716705 0.751767 0.661187E-01 0.716705 0.903373 1.16028 0.257578 0.903373 0.767990 0.948247 0.109957 0.767990 0.683811 0.601365 0.438290E-01 0.683811 1.29943 0.667067 0.633966 1.29943 TEST0745 For the Frechet PDF: FRECHET_MEAN computes the mean; FRECHET_SAMPLE samples; FRECHET_VARIANCE computes the variance. PDF parameter ALPHA = 3.00000 PDF mean = 1.35412 PDF variance = 0.845303 Sample size = 1000 Sample mean = 1.35005 Sample variance = 0.619220 Sample maximum = 7.81659 Sample minimum = 0.541476 TEST075 GAMMA evaluates the Gamma function; GAMMA_LOG evaluates the log of the Gamma function; GAMMA_LOG_INT evaluates the log for integer argument; I_FACTORIAL evaluates the factorial function. X, GAMMA(X), Exp(GAMMA_LOG(X)), Exp(GAMMA_LOG_INT(X)) I_FACTORIAL(X+1) 1.00000 1.00000 1.00000 1.00000 1.00000 2.00000 1.00000 1.00000 1.00000 1.00000 3.00000 2.00000 2.00000 2.00000 2.00000 4.00000 6.00000 6.00000 6.00000 6.00000 5.00000 24.0000 24.0000 24.0000 24.0000 6.00000 120.000 120.000 120.000 120.000 7.00000 720.000 720.000 720.000 720.000 8.00000 5040.00 5040.00 5040.00 5040.00 9.00000 40320.0 40320.0 40320.0 40320.0 10.0000 362880. 362880. 362880. 362880. TEST076: GAMMA_INC evaluates the normalized incomplete Gamma function P(A,X). GAMMA_INC_VALUES returns some exact values. A X Exact F GAMMA_INC(A,X) 0.1000 0.0300 2.49030 0.738235 0.1000 0.3000 0.871837 0.908358 0.1000 1.5000 0.107921 0.988656 0.5000 0.0750 1.23812 0.301465 0.5000 0.7500 0.391130 0.779329 0.5000 3.5000 0.144472E-01 0.991849 1.0000 0.1000 0.904837 0.951626E-01 1.0000 1.0000 0.367879 0.632121 1.0000 5.0000 0.673795E-02 0.993262 1.1000 0.1000 0.882797 0.720597E-01 1.1000 1.0000 0.390833 0.589181 1.1000 5.0000 0.805146E-02 0.991537 2.0000 0.1500 0.989814 0.101858E-01 2.0000 1.5000 0.557825 0.442175 2.0000 7.0000 0.729506E-02 0.992705 6.0000 2.5000 114.957 0.420210E-01 6.0000 12.0000 2.44092 0.979659 11.0000 16.0000 280855. 0.922604 26.0000 25.0000 0.857648E+25 0.447079 41.0000 45.0000 0.208503E+48 0.744455 TEST077 For the Gamma PDF: GAMMA_CDF evaluates the CDF. GAMMA_PDF evaluates the PDF. GAMMA_SAMPLE samples the PDF. PDF parameter A = 1.00000 PDF parameter B = 1.50000 PDF parameter C = 3.00000 X PDF CDF 9.78938 0.326457E-01 0.931465 3.71255 0.178685 0.271620 2.87613 0.149289 0.131701 6.15383 0.126698 0.667132 8.36485 0.592491E-01 0.867551 7.65229 0.777327E-01 0.818961 7.07259 0.953344E-01 0.768902 1.63088 0.387193E-01 0.907590E-02 6.51620 0.113991 0.710734 4.76846 0.170586 0.459340 TEST078 For the Gamma PDF: GAMMA_MEAN computes the mean; GAMMA_SAMPLE samples; GAMMA_VARIANCE computes the 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 = 7.03579 Sample variance = 19.6481 Sample maximum = 32.6521 Sample minimum = 1.19639 TEST079 For the Generalized Logistic PDF: GENLOGISTIC_PDF evaluates the PDF. GENLOGISTIC_CDF evaluates the CDF; GENLOGISTIC_CDF_INV inverts the CDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 X PDF CDF CDF_INV 1.82954 0.130320 0.218418 1.82954 9.39944 0.211989E-01 0.956318 9.39944 6.48873 0.751605E-01 0.829509 6.48873 4.10241 0.147371 0.561695 4.10241 3.15571 0.158177 0.415307 3.15571 0.225390 0.590738E-01 0.661187E-01 0.225390 2.11836 0.140536 0.257578 2.11836 0.832536 0.859182E-01 0.109957 0.832536 -0.215463 0.425639E-01 0.438290E-01 -0.215463 4.61496 0.134030 0.633966 4.61496 TEST080 For the Generalized Logistic PDF: GENLOGISTIC_MEAN computes the mean; GENLOGISTIC_SAMPLE samples; GENLOGISTIC_VARIANCE computes the 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 = 4.00819 Sample variance = 8.13473 Sample maximum = 15.5340 Sample minimum = -2.93789 TEST081 For the Geometric PDF: GEOMETRIC_CDF evaluates the CDF; GEOMETRIC_CDF_INV inverts the CDF. GEOMETRIC_PDF evaluates the PDF; PDF parameter A = 0.250000 X PDF CDF CDF_INV 1 0.250000 0.250000 2 11 0.140784E-01 0.957765 12 7 0.444946E-01 0.866516 8 3 0.140625 0.578125 4 2 0.187500 0.437500 3 1 0.250000 0.250000 2 2 0.187500 0.437500 3 1 0.250000 0.250000 2 1 0.250000 0.250000 2 4 0.105469 0.683594 5 TEST082 For the Geometric PDF: GEOMETRIC_MEAN computes the mean; GEOMETRIC_SAMPLE samples; GEOMETRIC_VARIANCE computes the variance. PDF parameter A = 0.250000 PDF mean = 4.00000 PDF variance = 12.0000 Sample size = 1000 Sample mean = 4.02200 Sample variance = 11.7413 Sample maximum = 22 Sample minimum = 1 TEST083 For the Geometric PDF: GEOMETRIC_PDF evaluates the PDF. GEOMETRIC_CDF evaluates the CDF. PDF parameter A = 0.250000 X PDF(X) CDF(X) 0 0.00000 0.00000 1 0.250000 0.250000 2 0.187500 0.437500 3 0.140625 0.578125 4 0.105469 0.683594 5 0.791016E-01 0.762695 6 0.593262E-01 0.822021 7 0.444946E-01 0.866516 8 0.333710E-01 0.899887 9 0.250282E-01 0.924915 10 0.187712E-01 0.943686 TEST084 For the Gompertz PDF: GOMPERTZ_CDF evaluates the CDF; GOMPERTZ_CDF_INV inverts the CDF. GOMPERTZ_PDF evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 0.798917E-01 2.47825 0.218418 0.798917E-01 0.785233 0.225843 0.956318 0.785233 0.494408 0.720533 0.829509 0.494408 0.251663 1.56551 0.561695 0.251663 0.168638 1.97158 0.415307 0.168638 0.226237E-01 2.84592 0.661187E-01 0.226237E-01 0.960122E-01 2.38054 0.257578 0.960122E-01 0.383151E-01 2.74199 0.109957 0.383151E-01 0.148627E-01 2.89822 0.438290E-01 0.148627E-01 0.301249 1.35309 0.633966 0.301249 TEST085 For the Gompertz PDF: GOMPERTZ_SAMPLE samples; PDF parameter A = 2.00000 PDF parameter B = 3.00000 Sample size = 1000 Sample mean = 0.279586 Sample variance = 0.569063E-01 Sample maximum = 1.27830 Sample minimum = 0.613224E-03 TEST086 For the Gumbel PDF: GUMBEL_CDF evaluates the CDF. GUMBEL_CDF_INV inverts the CDF. GUMBEL_PDF evaluates the PDF. X PDF CDF CDF_INV -0.419594 0.332289 0.218418 -0.419594 3.10856 0.427141E-01 0.956318 3.10856 1.67707 0.155053 0.829509 1.67707 0.550268 0.323983 0.561695 0.550268 0.129270 0.364946 0.415307 0.129270 -0.999272 0.179599 0.661187E-01 -0.999272 -0.304859 0.349387 0.257578 -0.304859 -0.791937 0.242748 0.109957 -0.791937 -1.14022 0.137073 0.438290E-01 -1.14022 0.785788 0.288936 0.633966 0.785788 TEST087 For the Gumbel PDF: GUMBEL_MEAN computes the mean; GUMBEL_SAMPLE samples; GUMBEL_VARIANCE computes the variance. PDF mean = 0.577216 PDF variance = 1.64493 Sample size = 1000 Sample mean = 0.581659 Sample variance = 1.63026 Sample maximum = 6.16874 Sample minimum = -1.84037 TEST088 For the Half Normal PDF: HALF_NORMAL_CDF evaluates the CDF. HALF_NORMAL_CDF_INV inverts the CDF. HALF_NORMAL_PDF evaluates the PDF. PDF parameter A = 0.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 0.554517 0.383899 0.218418 0.554517 4.03425 0.521654E-01 0.956318 4.03425 2.74126 0.155945 0.829509 2.74126 1.55012 0.295438 0.561695 1.55012 1.09309 0.343595 0.415307 1.09309 0.165925 0.397572 0.661187E-01 0.165925 0.657295 0.377969 0.257578 0.657295 0.276499 0.395148 0.109957 0.276499 0.109918 0.398340 0.438290E-01 0.109918 1.80785 0.265145 0.633966 1.80785 TEST089 For the Half Normal PDF: HALF_NORMAL_MEAN computes the mean; HALF_NORMAL_SAMPLE samples; HALF_NORMAL_VARIANCE computes the variance. PDF parameter A = 0.00000 PDF parameter B = 10.0000 PDF mean = 7.97885 PDF variance = 36.3380 Sample size = 1000 Sample mean = 8.01612 Sample variance = 35.9155 Sample maximum = 30.7690 Sample minimum = 0.230406E-01 TEST090 For the Hypergeometric PDF: HYPERGEOMETRIC_CDF evaluates the CDF. HYPERGEOMETRIC_PDF evaluates the PDF. Total number of balls = 1000 Number of white balls = 70 Number of balls taken = 100 PDF argument X = 7 PDF value = = 0.162835 CDF value = = 0.599487 TEST091 For the Hypergeometric PDF: HYPERGEOMETRIC_MEAN computes the mean; HYPERGEOMETRIC_SAMPLE samples; HYPERGEOMETRIC_VARIANCE computes the variance. PDF parameter N = 100 PDF parameter M = 70 PDF parameter L = 1000 PDF mean = 7.00000 PDF variance = 1.56560 THIS CALL IS TAKING FOREVER! TEST092 R8_CEILING rounds an R8 up. X R8_CEILING(X) -1.20000 0 -1.00000 0 -0.800000 0 -0.600000 0 -0.400000 0 -0.200000 0 0.00000 0 0.200000 0 0.400000 0 0.600000 0 0.800000 0 1.00000 0 1.20000 0 TEST093 For the Inverse Gaussian PDF: INVERSE_GAUSSIAN_CDF evaluates the CDF. INVERSE_GAUSSIAN_PDF evaluates the PDF. PDF parameter A = 5.00000 PDF parameter B = 2.00000 X PDF CDF 0.559532 0.329239 0.861168E-01 2.40685 0.135119 0.515034 0.909740 0.311588 0.201254 2.19648 0.150200 0.485064 0.566488 0.330272 0.884105E-01 0.471548 0.305960 0.580219E-01 5.32365 0.458954E-01 0.744699 0.780629 0.328531 0.159870 3.24717 0.928392E-01 0.609153 2.78698 0.113031 0.562013 TEST094 For the Inverse Gaussian PDF: INVERSE_GAUSSIAN_MEAN computes the mean; INVERSE_GAUSSIAN_SAMPLE samples; INVERSE_GAUSSIAN_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 2.66667 Sample size = 1000 Sample mean = 1.98986 Sample variance = 2.72314 Sample maximum = 13.5187 Sample minimum = 0.215551 TEST095 For the Laplace PDF: LAPLACE_CDF evaluates the CDF; LAPLACE_CDF_INV inverts the CDF. LAPLACE_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV -0.656392 0.109209 0.218418 -0.656392 5.87532 0.218412E-01 0.956318 5.87532 3.15185 0.852454E-01 0.829509 3.15185 1.26339 0.219152 0.561695 1.26339 0.628820 0.207654 0.415307 0.628820 -3.04631 0.330594E-01 0.661187E-01 -3.04631 -0.326573 0.128789 0.257578 -0.326573 -2.02904 0.549784E-01 0.109957 -2.02904 -3.86862 0.219145E-01 0.438290E-01 -3.86862 1.62376 0.183017 0.633966 1.62376 TEST096 For the Laplace PDF: LAPLACE_MEAN computes the mean; LAPLACE_SAMPLE samples; LAPLACE_VARIANCE computes the variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF mean = 1.00000 PDF variance = 8.00000 Sample size = 1000 Sample mean = 0.994018 Sample variance = 8.10829 Sample maximum = 11.9533 Sample minimum = -10.2115 TEST0965 For the Levy PDF: LEVY_CDF evaluates the CDF; LEVY_CDF_INV inverts the CDF. LEVY_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 X PDF CDF X2 2.32036 0.174367 0.218418 2.32036 667.596 0.327326E-04 0.956318 667.596 44.1337 0.194595E-02 0.829509 44.1337 6.93865 0.329430E-01 0.561695 6.93865 4.01406 0.773762E-01 0.415307 4.01406 1.59227 0.228757 0.661187E-01 1.59227 2.56039 0.152493 0.257578 2.56039 1.78283 0.227065 0.109957 1.78283 1.49223 0.214227 0.438290E-01 1.49223 9.82141 0.192259E-01 0.633966 9.82141 TEST097 For the Logistic PDF: LOGISTIC_CDF evaluates the CDF; LOGISTIC_CDF_INV inverts the CDF. LOGISTIC_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV -1.54982 0.853559E-01 0.218418 -1.54982 7.17229 0.208871E-01 0.956318 7.17229 4.16431 0.707118E-01 0.829509 4.16431 1.49609 0.123097 0.561695 1.49609 0.315863 0.121414 0.415307 0.315863 -4.29579 0.308735E-01 0.661187E-01 -4.29579 -1.11719 0.956157E-01 0.257578 -1.11719 -3.18237 0.489331E-01 0.109957 -3.18237 -5.16528 0.209540E-01 0.438290E-01 -5.16528 2.09854 0.116027 0.633966 2.09854 TEST098 For the Logistic PDF: LOGISTIC_MEAN computes the mean; LOGISTIC_SAMPLE samples; LOGISTIC_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 29.6088 Sample size = 1000 Sample mean = 2.00703 Sample variance = 29.8759 Sample maximum = 20.5031 Sample minimum = -16.8911 TEST099 For the Lognormal PDF: LOG_NORMAL_CDF evaluates the CDF; LOG_NORMAL_CDF_INV inverts the CDF. LOG_NORMAL_PDF evaluates the PDF; PDF parameter A = 10.0000 PDF parameter B = 2.25000 X PDF CDF CDF_INV 3829.62 0.342207E-04 0.218418 3829.62 0.103126E+07 0.398836E-07 0.956318 0.103126E+07 187683. 0.600352E-06 0.829509 187683. 31236.9 0.560821E-05 0.561695 31236.9 13611.8 0.127314E-04 0.415307 13611.8 744.708 0.766792E-04 0.661187E-01 744.708 5093.04 0.281690E-04 0.257578 5093.04 1393.81 0.599421E-04 0.109957 1393.81 472.134 0.873521E-04 0.438290E-01 472.134 47588.4 0.351376E-05 0.633966 47588.4 TEST100 For the Lognormal PDF: LOG_NORMAL_MEAN computes the mean; LOG_NORMAL_SAMPLE samples; LOG_NORMAL_VARIANCE computes the variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF mean = 20.0855 PDF variance = 21623.0 Sample size = 1000 Sample mean = 18.2209 Sample variance = 3776.12 Sample maximum = 835.466 Sample minimum = 0.815371E-02 TEST101 For the Logseries PDF, LOG_SERIES_CDF evaluates the CDF; LOG_SERIES_CDF_INV inverts the CDF. LOG_SERIES_PDF evaluates the PDF; PDF parameter A = 0.250000 X PDF CDF CDF_INV 1 0.869015 0.869015 2 1 0.869015 0.869015 2 2 0.108627 0.977642 3 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 1 0.869015 0.869015 2 4 0.339459E-02 0.999141 5 1 0.869015 0.869015 2 2 0.108627 0.977642 3 TEST102 For the Logseries PDF: LOG_SERIES_CDF evaluates the CDF; LOG_SERIES_PDF evaluates the PDF. PDF parameter A = 0.250000 X PDF(X) CDF(X) 1 0.869015 0.869015 2 0.108627 0.977642 3 0.181045E-01 0.995746 4 0.339459E-02 0.999141 5 0.678918E-03 0.999820 6 0.141441E-03 0.999961 7 0.303088E-04 0.999991 8 0.663006E-05 0.999998 9 0.147335E-05 1.00000 10 0.331503E-06 1.00000 TEST103 For the Logseries PDF: LOG_SERIES_MEAN computes the mean; LOG_SERIES_VARIANCE computes the variance; LOG_SERIES_SAMPLE samples. PDF parameter A = 0.250000 PDF mean = 1.15869 PDF variance = 0.202361 Sample size = 1000 Sample mean = 1.16500 Sample variance = 0.213989 Sample maximum = 4 Sample minimum = 1 TEST104 For the Log Uniform PDF: LOG_UNIFORM_CDF evaluates the CDF; LOG_UNIFORM_CDF_INV inverts the CDF. LOG_UNIFORM_PDF evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 20.0000 X PDF CDF CDF_INV 3.30711 0.131322 0.218418 3.30711 18.0862 0.240125E-01 0.956318 18.0862 13.5064 0.321547E-01 0.829509 13.5064 7.28996 0.595743E-01 0.561695 7.28996 5.20400 0.834540E-01 0.415307 5.20400 2.32889 0.186481 0.661187E-01 2.32889 3.61916 0.119999 0.257578 3.61916 2.57624 0.168577 0.109957 2.57624 2.21238 0.196302 0.438290E-01 2.21238 8.60985 0.504416E-01 0.633966 8.60985 TEST105 For the Log Uniform PDF: LOG_UNIFORM_MEAN computes the mean; LOG_UNIFORM_SAMPLE samples; PDF parameter A = 2.00000 PDF parameter B = 20.0000 PDF mean = 7.81730 Sample size = 1000 Sample mean = 7.84210 Sample variance = 24.5202 Sample maximum = 19.9039 Sample minimum = 2.00848 TEST106 For the Lorentz PDF: LORENTZ_CDF evaluates the CDF; LORENTZ_CDF_INV inverts the CDF. LORENTZ_PDF evaluates the PDF; X PDF CDF CDF_INV -1.22110 0.127780 0.218418 -1.22110 7.24111 0.595711E-02 0.956318 7.24111 1.68497 0.829119E-01 0.829509 1.68497 0.196286 0.306501 0.561695 0.196286 -0.272532 0.296302 0.415307 -0.272532 -4.74478 0.135377E-01 0.661187E-01 -4.74478 -0.953486 0.166730 0.257578 -0.953486 -2.77879 0.364964E-01 0.109957 -2.77879 -7.21659 0.599690E-02 0.438290E-01 -7.21659 0.447611 0.265180 0.633966 0.447611 TEST107 For the Lorentz PDF: LORENTZ_MEAN computes the mean; LORENTZ_VARIANCE computes the variance; LORENTZ_SAMPLE samples. PDF mean = 0.00000 PDF variance = 0.100000E+31 Sample size = 1000 Sample mean = -0.111859 Sample variance = 175.490 Sample maximum = 152.177 Sample minimum = -173.146 TEST108 For the Maxwell CDF: MAXWELL_CDF evaluates the CDF. MAXWELL_CDF_INV inverts the CDF. MAXWELL_PDF evaluates the PDF. PDF parameter A = 2.00000 X PDF CDF CDF_INV 3.66776 0.249667 0.700353 3.66797 2.69139 0.292127 0.558307 2.69141 4.68560 0.140774 0.803679 4.68555 6.01636 0.391311E-01 0.889183 6.01562 3.01933 0.290920 0.611345 3.01953 0.930238 0.774572E-01 0.181875 0.930176 4.38454 0.173412 0.777177 4.38477 4.19739 0.194258 0.759077 4.19727 4.11671 0.203205 0.750866 4.11719 3.57428 0.258040 0.688745 3.57422 TEST109 For the Maxwell PDF: MAXWELL_MEAN computes the mean; MAXWELL_VARIANCE computes the variance; MAXWELL_SAMPLE samples. PDF parameter A = 2.00000 PDF mean = 3.19154 PDF mean = 1.81408 Sample size = 1000 Sample mean = 3.16297 Sample variance = 1.78593 Sample maximum = 7.34277 Sample minimum = 0.353604 TEST110 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 TEST111 For the Multinomial PDF: MULTINOMIAL_MEAN computes the mean; MULTINOMIAL_SAMPLE samples; MULTINOMIAL_VARIANCE computes the 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 0.628000 0.552168 0 3 2 2.47200 1.23445 0 5 3 1.90000 1.20721 0 5 TEST112 For the Multinomial PDF: MULTINOMIAL_PDF evaluates the 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 TEST113 For the Nakagami PDF: NAKAGAMI_CDF evaluates the CDF; NAKAGAMI_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF argument X = 1.25000 PDF value = 0.393121E-03 CDF value = 0.165738E-04 TEST114 For the Nakagami PDF: NAKAGAMI_MEAN computes the mean; NAKAGAMI_VARIANCE computes the variance. PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF mean = 2.91874 PDF variance = 0.318446 TEST1145 For the Negative Binomial PDF: NEGATIVE_BINOMIAL_CDF evaluates the CDF. NEGATIVE_BINOMIAL_CDF_INV inverts the CDF. NEGATIVE_BINOMIAL_PDF evaluates the PDF. PDF parameter A = 2 PDF parameter B = 0.250000 X PDF CDF CDF_INV 6 0.988770E-01 0.466064 6 3 0.937500E-01 0.156250 3 7 0.889893E-01 0.555054 7 4 0.105469 0.261719 4 4 0.105469 0.261719 4 13 0.316764E-01 0.873295 13 8 0.778656E-01 0.632919 8 6 0.988770E-01 0.466064 6 12 0.387155E-01 0.841618 12 6 0.988770E-01 0.466064 6 TEST1146 For the Negative Binomial PDF: NEGATIVE_BINOMIAL_MEAN computes the mean; NEGATIVE_BINOMIAL_SAMPLE samples; NEGATIVE_BINOMIAL_VARIANCE computes the variance. PDF parameter A = 2 PDF parameter B = 0.750000 PDF mean = 2.66667 PDF variance = 0.888889 Sample size = 1000 Sample mean = 2.68800 Sample variance = 0.833489 Sample maximum = 8 Sample minimum = 2 TEST115 For the Normal 01 PDF: NORMAL_01_CDF evaluates the CDF; NORMAL_01_CDF_INV inverts the CDF. NORMAL_01_PDF evaluates the PDF; X PDF CDF CDF_INV 1.679040256736491 0.974392E-01 0.953428 1.679040256746338 -0.4727688004888129 0.356759 0.318189 -0.4727688004855372 -0.5660598123302577 0.339884 0.285677 -0.5660598123353983 -0.2311241308033988 0.388428 0.408609 -0.2311241308099739 1.212934217379310 0.191179 0.887423 1.212934217394378 0.5350371373557014 0.345739 0.703688 0.5350371373577746 1.269380628984426 0.178244 0.897847 1.269380629005457 1.049542669494471 0.229993 0.853036 1.049542669511194 -1.666086672831968 0.995733E-01 0.478481E-01 -1.666086672843646 -1.865227723476435 0.700549E-01 0.310747E-01 -1.865227723463066 TEST116 For the Normal 01 PDF: NORMAL_01_MEAN computes the mean; NORMAL_01_SAMPLE samples the PDF; NORMAL_01_VARIANCE returns the variance. PDF mean = 0.00000 PDF variance = 1.00000 Sample size = 1000 Sample mean = -0.169444E-01 Sample variance = 0.999622 Sample maximum = 3.32858 Sample minimum = -3.02975 TEST117 For the Normal PDF: NORMAL_CDF evaluates the CDF; NORMAL_CDF_INV inverts the CDF. NORMAL_PDF evaluates the PDF; PDF parameter A = 100.000 PDF parameter B = 15.0000 X PDF CDF CDF_INV 125.186 0.649595E-02 0.953428 125.186 92.9085 0.237840E-01 0.318189 92.9085 91.5091 0.226589E-01 0.285677 91.5091 96.5331 0.258952E-01 0.408609 96.5331 118.194 0.127453E-01 0.887423 118.194 108.026 0.230493E-01 0.703688 108.026 119.041 0.118829E-01 0.897847 119.041 115.743 0.153328E-01 0.853036 115.743 75.0087 0.663822E-02 0.478481E-01 75.0087 72.0216 0.467033E-02 0.310747E-01 72.0216 TEST118 For the Normal PDF: NORMAL_MEAN computes the mean; NORMAL_SAMPLE samples; NORMAL_VARIANCE returns the variance. PDF parameter A = 100.000 PDF parameter B = 15.0000 PDF mean = 100.000 PDF variance = 225.000 Sample size = 1000 Sample mean = 99.7458 Sample variance = 224.915 Sample maximum = 149.929 Sample minimum = 54.5537 TEST1184 For the Truncated Normal PDF: NORMAL_TRUNCATED_AB_CDF evaluates the CDF. NORMAL_TRUNCATED_AB_CDF_INV inverts the CDF. NORMAL_TRUNCATED_AB_PDF evaluates the 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 81.6300 0.127629E-01 0.218418 81.6300 137.962 0.527826E-02 0.956318 137.962 122.367 0.112043E-01 0.829509 122.367 103.704 0.165359E-01 0.561695 103.704 94.8990 0.163740E-01 0.415307 94.8990 65.8326 0.657044E-02 0.661187E-01 65.8326 84.5743 0.138204E-01 0.257578 84.5743 71.5672 0.875626E-02 0.109957 71.5672 62.0654 0.528716E-02 0.438290E-01 62.0654 108.155 0.158521E-01 0.633966 108.155 TEST1185 For the Truncated Normal PDF: NORMAL_TRUNCATED_AB_MEAN computes the mean; NORMAL_TRUNCATED_AB_SAMPLE samples; NORMAL_TRUNCATED_AB_VARIANCE computes the 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 = 100.123 Sample variance = 486.064 Sample maximum = 149.108 Sample minimum = 50.7873 TEST1186 For the Lower Truncated Normal PDF: NORMAL_TRUNCATED_A_CDF evaluates the CDF. NORMAL_TRUNCATED_A_CDF_INV inverts the CDF. NORMAL_TRUNCATED_A_PDF evaluates the 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 82.0355 0.126136E-01 0.218418 82.0355 143.008 0.371817E-02 0.956318 143.008 124.191 0.102245E-01 0.829509 124.191 104.515 0.160650E-01 0.561695 104.515 95.5021 0.160670E-01 0.415307 95.5021 66.0709 0.650134E-02 0.661187E-01 66.0709 85.0161 0.136446E-01 0.257578 85.0161 71.8645 0.866826E-02 0.109957 71.8645 62.2618 0.522585E-02 0.438290E-01 62.2618 109.115 0.152792E-01 0.633966 109.115 TEST1187 For the Lower Truncated Normal PDF: NORMAL_TRUNCATED_A_MEAN computes the mean; NORMAL_TRUNCATED_A_SAMPLE samples; NORMAL_TRUNCATED_A_VARIANCE computes the variance. The "parent" normal distribution has mean = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [ 50.0000 ,+oo] PDF mean = 101.381 PDF variance = 554.032 Sample size = 1000 Sample mean = 101.504 Sample variance = 555.665 Sample maximum = 171.782 Sample minimum = 50.8055 TEST1188 For the Upper Truncated Normal PDF: NORMAL_TRUNCATED_B_CDF evaluates the CDF. NORMAL_TRUNCATED_B_CDF_INV inverts the CDF. NORMAL_TRUNCATED_B_PDF evaluates the 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 80.1372 0.119094E-01 0.218418 80.1372 137.766 0.521699E-02 0.956318 137.766 122.006 0.110844E-01 0.829509 122.006 103.073 0.162063E-01 0.561695 103.073 94.0447 0.158724E-01 0.415307 94.0447 62.0713 0.516592E-02 0.661187E-01 62.0713 83.2727 0.130542E-01 0.257578 83.2727 68.9956 0.756806E-02 0.109957 68.9956 57.0318 0.372825E-02 0.438290E-01 57.0318 107.607 0.155905E-01 0.633966 107.607 TEST1189 For the Upper Truncated Normal PDF: NORMAL_TRUNCATED_B_MEAN computes the mean; NORMAL_TRUNCATED_B_SAMPLE samples; NORMAL_TRUNCATED_B_VARIANCE computes the variance. The "parent" normal distribution has mean = 100.000 standard deviation = 25.0000 The parent distribution is truncated to the interval [-oo, 150.000 ] PDF mean = 98.6188 PDF variance = 554.032 Sample size = 1000 Sample mean = 98.7101 Sample variance = 560.281 Sample maximum = 149.087 Sample minimum = 27.2041 TEST119 For the Pareto PDF: PARETO_CDF evaluates the CDF; PARETO_CDF_INV inverts the CDF. PARETO_PDF evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 2.17123 1.07992 0.218418 2.17123 5.67886 0.230763E-01 0.956318 5.67886 3.60686 0.141805 0.829509 3.60686 2.63292 0.499412 0.561695 2.63292 2.39178 0.733379 0.415307 2.39178 2.04613 1.36924 0.661187E-01 2.04613 2.20875 1.00838 0.257578 2.20875 2.07918 1.28422 0.109957 2.07918 2.03010 1.41299 0.438290E-01 2.03010 2.79591 0.392754 0.633966 2.79591 TEST120 For the Pareto PDF: PARETO_MEAN computes the mean; PARETO_SAMPLE samples; PARETO_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 3.00000 PDF variance = 3.00000 Sample size = 1000 Sample mean = 2.99105 Sample variance = 2.10266 Sample maximum = 15.6386 Sample minimum = 2.00123 TEST123 For the Pearson 05 PDF: PEARSON_05_PDF evaluates the 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 TEST124 For the Planck PDF: PLANCK_PDF evaluates the PDF. PLANCK_SAMPLE samples the PDF. PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF 3.67300 0.788188E-01 0.667852 0.261867 4.15261 0.436289E-01 2.32528 0.298879 1.96150 0.375246 1.14325 0.416449 4.18500 0.418554E-01 0.920753 0.362470 1.68781 0.419450 2.37886 0.287218 TEST125 For the Planck PDF: PLANCK_MEAN computes the mean. PLANCK_SAMPLE samples. PLANCK_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 3.83223 PDF variance = 4.11326 Sample size = 1000 Sample mean = 1.95188 Sample variance = 1.08647 Sample maximum = 7.50765 Sample minimum = 0.177481 TEST126: POISSON_CDF evaluates the cumulative distribution function for the discrete Poisson probability density function. POISSON_CDF_VALUES returns some exact values. A is the expected mean number of successes per unit time; X is the number of successes; POISSON_CDF is the probability of having up to X successes in unit time. A X Exact F POISSON_CDF(A,X) 0.0200 0 0.980199 0.980199 0.1000 0 0.904837 0.904837 0.1000 1 0.995321 0.995321 0.5000 0 0.606531 0.606531 0.5000 1 0.909796 0.909796 0.5000 2 0.985612 0.985612 1.0000 0 0.367879 0.367879 1.0000 1 0.735759 0.735759 1.0000 2 0.919699 0.919699 1.0000 3 0.981012 0.981012 2.0000 0 0.135335 0.135335 2.0000 1 0.406006 0.406006 2.0000 2 0.676676 0.676676 2.0000 3 0.857123 0.857123 5.0000 0 0.673795E-02 0.673795E-02 5.0000 1 0.404277E-01 0.404277E-01 5.0000 2 0.124652 0.124652 5.0000 3 0.265026 0.265026 5.0000 4 0.440493 0.440493 5.0000 5 0.615961 0.615961 5.0000 6 0.762183 0.762183 TEST127 For the Poisson PDF: POISSON_CDF evaluates the CDF, POISSON_CDF_INV inverts the CDF. POISSON_PDF evaluates the PDF. PDF parameter A = 10.0000 X PDF CDF CDF_INV 7 0.900792E-01 0.220221 7 16 0.216988E-01 0.972958 16 13 0.729079E-01 0.864464 13 10 0.125110 0.583040 10 9 0.125110 0.457930 9 5 0.378333E-01 0.670860E-01 5 8 0.112599 0.332820 8 6 0.630555E-01 0.130141 6 5 0.378333E-01 0.670860E-01 5 11 0.113736 0.696776 11 TEST128 For the Poisson PDF: POISSON_MEAN computes the mean; POISSON_SAMPLE samples; POISSON_VARIANCE computes the variance. PDF parameter A = 10.0000 PDF mean = 10.0000 PDF variance = 10.0000 Sample size = 1000 Sample mean = 10.0050 Sample variance = 10.0050 Sample maximum = 20 Sample minimum = 2 TEST129 For the Power PDF: POWER_CDF evaluates the CDF; POWER_CDF_INV inverts the CDF. POWER_PDF evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 1.40206 0.311568 0.218418 1.40206 2.93374 0.651943 0.956318 2.93374 2.73232 0.607183 0.829509 2.73232 2.24839 0.499642 0.561695 2.24839 1.93333 0.429629 0.415307 1.93333 0.771407 0.171424 0.661187E-01 0.771407 1.52256 0.338347 0.257578 1.52256 0.994792 0.221065 0.109957 0.994792 0.628061 0.139569 0.438290E-01 0.628061 2.38866 0.530813 0.633966 2.38866 TEST130 For the Power PDF: POWER_MEAN computes the mean; POWER_SAMPLE samples; POWER_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF variance = 0.500000 Sample size = 1000 Sample mean = 2.00568 Sample variance = 0.505123 Sample maximum = 2.99686 Sample minimum = 0.128629 TEST1304 For the Quasigeometric PDF: QUASIGEOMETRIC_CDF evaluates the CDF; QUASIGEOMETRIC_CDF_INV inverts the CDF. QUASIGEOMETRIC_PDF evaluates the PDF; PDF parameter A = 0.482500 PDF parameter B = 0.589300 X PDF CDF CDF_INV 0 0.482500 0.482500 1 5 0.256319E-01 0.963222 6 3 0.738088E-01 0.894094 4 1 0.212537 0.695037 2 0 0.482500 0.482500 1 0 0.482500 0.482500 1 0 0.482500 0.482500 1 0 0.482500 0.482500 1 0 0.482500 0.482500 1 1 0.212537 0.695037 2 TEST1306 For the Quasigeometric PDF: QUASIGEOMETRIC_MEAN computes the mean; QUASIGEOMETRIC_SAMPLE samples; QUASIGEOMETRIC_VARIANCE computes the variance. PDF parameter A = 0.482500 PDF parameter B = 0.589300 PDF mean = 1.26004 PDF variance = 3.28832 Sample size = 1000 Sample mean = 1.26700 Sample variance = 3.21693 Sample maximum = 11 Sample minimum = 0 TEST131 For the Rayleigh PDF: RAYLEIGH_CDF evaluates the CDF; RAYLEIGH_CDF_INV inverts the CDF. RAYLEIGH_PDF evaluates the PDF; PDF parameter A = 2.00000 X PDF CDF CDF_INV 1.40410 0.274354 0.218418 1.40410 5.00465 0.546538E-01 0.956318 5.00465 3.76199 0.160346 0.829509 3.76199 2.56880 0.281479 0.561695 2.56880 2.07204 0.302877 0.415307 2.07204 0.739762 0.172712 0.661187E-01 0.739762 1.54360 0.286501 0.257578 1.54360 0.965340 0.214799 0.109957 0.965340 0.598789 0.143136 0.438290E-01 0.598789 2.83553 0.259475 0.633966 2.83553 TEST132 For the Rayleigh PDF: RAYLEIGH_MEAN computes the mean; RAYLEIGH_SAMPLE samples; RAYLEIGH_VARIANCE computes the variance. PDF parameter A = 2.00000 PDF mean = 2.50663 PDF variance = 1.71681 Sample size = 1000 Sample mean = 2.51390 Sample variance = 1.70827 Sample maximum = 7.02555 Sample minimum = 0.121328 TEST133 For the Reciprocal PDF: RECIPROCAL_CDF evaluates the CDF. RECIPROCAL_CDF_INV inverts the CDF. RECIPROCAL_PDF evaluates the PDF. PDF parameter A = 1.00000 PDF parameter B = 3.00000 X PDF CDF CDF_INV 1.27119 0.716050 0.218418 1.27119 2.85943 0.318329 0.956318 2.85943 2.48758 0.365914 0.829509 2.48758 1.85352 0.491087 0.561695 1.85352 1.57816 0.576771 0.415307 1.57816 1.07534 0.846465 0.661187E-01 1.07534 1.32708 0.685898 0.257578 1.32708 1.12840 0.806664 0.109957 1.12840 1.04933 0.867449 0.438290E-01 1.04933 2.00668 0.453604 0.633966 2.00668 TEST134 For the Reciprocal PDF: RECIPROCAL_MEAN computes the mean; RECIPROCAL_SAMPLE samples; RECIPROCAL_VARIANCE computes the variance. PDF parameter A = 1.00000 PDF parameter B = 3.00000 PDF mean = 1.82048 PDF variance = 0.326815 Sample size = 1000 Sample mean = 1.82510 Sample variance = 0.321955 Sample maximum = 2.99311 Sample minimum = 1.00202 TEST1341: RIBESL computes values of Bessel functions of NONINTEGER order. BESSEL_IX_VALUES returns selected values of the Bessel function In for NONINTEGER order. ALPHA X FX FX2 (table) (RIBESL) 0.50000000 0.20000000 0.3592084175833614 0.3592084175833614 0.50000000 1.00000000 0.9376748882454876 0.9376748882454875 0.50000000 2.00000000 2.046236863089055 2.046236863089054 0.50000000 2.50000000 3.053093538196718 3.053093538196719 0.50000000 3.00000000 4.614822903407601 4.614822903407601 0.50000000 5.00000000 26.47754749755907 26.47754749755907 0.50000000 10.00000000 2778.784603874571 2778.784603874571 0.50000000 20.00000000 43279746.27242893 43279746.27242893 1.50000000 1.00000000 0.2935253263474798 0.2935253263474797 1.50000000 2.00000000 1.099473188633110 1.099473188633109 1.50000000 5.00000000 21.18444226479414 21.18444226479414 1.50000000 10.00000000 2500.906154942118 2500.906154942118 1.50000000 50.00000000 0.2866653715931464E+21 0.2866653715931463E+21 2.50000000 1.00000000 0.5709890920304825E-01 0.5709890920304823E-01 2.50000000 2.00000000 0.3970270801393905 0.3970270801393904 2.50000000 5.00000000 13.76688213868258 13.76688213868258 2.50000000 10.00000000 2028.512757391936 2028.512757391936 2.50000000 50.00000000 0.2753157630035402E+21 0.2753157630035401E+21 1.25000000 1.00000000 0.4139416015642352 0.4139416015642352 1.25000000 2.00000000 1.340196758982897 1.340196758982897 1.25000000 5.00000000 22.85715510364670 22.85715510364670 1.25000000 10.00000000 2593.006763432002 2593.006763432002 1.25000000 50.00000000 0.2886630075077766E+21 0.2886630075077766E+21 2.75000000 1.00000000 0.3590910483251082E-01 0.3590910483251082E-01 2.75000000 2.00000000 0.2931108636266483 0.2931108636266483 2.75000000 5.00000000 11.99397010023068 11.99397010023068 2.75000000 10.00000000 1894.575731562383 1894.575731562383 2.75000000 50.00000000 0.2716911375760483E+21 0.2716911375760485E+21 TEST1342 For the RUNS PDF: RUNS_PDF evaluates the 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 TEST1344 For the RUNS PDF: RUNS_MEAN computes the mean; RUNS_VARIANCE computes the variance PDF parameter M = 10 PDF parameter N = 5 PDF mean = 7.66667 PDF variance = 2.69841 Sample size = 1000 Sample mean = 7.65000 Sample variance = 2.61011 Sample maximum = 11 Sample minimum = 2 TEST135 For the Hyperbolic Secant PDF: SECH_CDF evaluates the CDF. SECH_CDF_INV inverts the CDF. SECH_PDF evaluates the PDF. PDF parameter A = 3.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 0.941182 0.100839 0.218418 0.941182 8.35531 0.217727E-01 0.956318 8.35531 5.58635 0.812276E-01 0.829509 5.58635 3.39009 0.156175 0.561695 3.39009 2.46147 0.153555 0.415307 2.46147 -1.52223 0.328221E-01 0.661187E-01 -1.52223 1.30380 0.115187 0.257578 1.30380 -0.492142 0.538915E-01 0.109957 -0.492142 -2.34859 0.218453E-01 0.438290E-01 -2.34859 3.86774 0.145266 0.633966 3.86774 TEST136 For the Hyperbolic Secant PDF: SECH_MEAN computes the mean; SECH_SAMPLE samples; SECH_VARIANCE computes the variance. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 3.00000 PDF variance = 9.86960 Sample size = 1000 Sample mean = 2.99951 Sample variance = 9.97628 Sample maximum = 14.4364 Sample minimum = -8.69458 TEST137 For the Semicircular PDF: SEMICIRCULAR_CDF evaluates the CDF. SEMICIRCULAR_CDF_INV inverts the CDF. SEMICIRCULAR_PDF evaluates the PDF. PDF parameter A = 3.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 2.07408 0.282143 0.216167 2.07422 2.64915 0.313374 0.388897 2.64941 4.26118 0.247045 0.872972 4.26123 3.95508 0.279670 0.792025 3.95508 2.82894 0.317143 0.445615 2.82910 3.07844 0.318065 0.524963 3.07861 2.09106 0.283538 0.220968 2.09082 4.78579 0.143324 0.979302 4.78516 3.85620 0.287667 0.763967 3.85645 3.61440 0.302918 0.692448 3.61426 TEST138 For the Semicircular PDF: SEMICIRCULAR_MEAN computes the mean; SEMICIRCULAR_SAMPLE samples; SEMICIRCULAR_VARIANCE computes the variance. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 3.00000 PDF variance = 1.00000 Sample size = 1000 Sample mean = 3.02688 Sample variance = 0.989554 Sample maximum = 4.96783 Sample minimum = 1.05174 TEST139: STUDENT_CDF evaluates the cumulative distribution function for the Student's central T probability density function. STUDENT_CDF_VALUES returns some exact values. A B C X Exact F STUDENT_CDF(A,B,C,X) 0.0000 1.0000 1.0000 0.3250 0.600023 0.600023 0.0000 1.0000 2.0000 0.2890 0.600108 0.600108 0.0000 1.0000 3.0000 0.2770 0.600115 0.600115 0.0000 1.0000 4.0000 0.2710 0.600100 0.600100 0.0000 1.0000 5.0000 0.2670 0.599934 0.599934 0.0000 1.0000 2.0000 0.8160 0.749886 0.749886 0.0000 1.0000 5.0000 0.7270 0.750088 0.750088 0.0000 1.0000 2.0000 2.9200 0.950000 0.950000 0.0000 1.0000 5.0000 2.0150 0.949997 0.949997 0.0000 1.0000 2.0000 6.9650 0.990001 0.990001 0.0000 1.0000 3.0000 4.5410 0.990002 0.990002 0.0000 1.0000 4.0000 3.7470 0.990000 0.990000 0.0000 1.0000 5.0000 3.3650 0.990001 0.990001 TEST140 For the central Student PDF: STUDENT_CDF evaluates the CDF. STUDENT_PDF evaluates the PDF. STUDENT_SAMPLE samples the PDF. PDF parameter A = 0.500000 PDF parameter B = 2.00000 PDF parameter C = 6.00000 X PDF CDF 2.57394 0.131079 0.830139 0.876652 0.368348 0.571585 1.15653 0.340916 0.623068 0.297695 0.378517 0.461363 0.287044 0.378065 0.459337 0.307008 0.378894 0.463135 0.112830 0.367552 0.426444 0.253776 0.376508 0.453019 0.521450 0.382685 0.504105 0.493987 0.382729 0.498849 TEST141 For the central Student PDF: STUDENT_MEAN computes the mean; STUDENT_SAMPLE samples; STUDENT_VARIANCE computes the 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 = 0.373969 Sample variance = 3.06700 Sample maximum = 6.66826 Sample minimum = -23.2899 TEST142 For the Noncentral Student PDF: STUDENT_NONCENTRAL_CDF evaluates the CDF; PDF argument X = 0.500000 PDF parameter IDF = 10 PDF parameter B = 1.00000 CDF value = 0.305280 TEST1425 TFN evaluates Owen's T function; OWEN_VALUES stores some exact values. H A T(H,A) Exact 0.625000E-01 0.250000 0.389119E-01 0.389119E-01 6.50000 0.437500 0.200058E-10 0.200058E-10 7.00000 0.968750 0.639906E-12 0.639906E-12 4.78125 0.625000E-01 0.106330E-06 0.106330E-06 2.00000 0.500000 0.862508E-02 0.862508E-02 1.00000 0.999997 0.667418E-01 0.667418E-01 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 TEST143 For the Triangle PDF: TRIANGLE_CDF evaluates the CDF; TRIANGLE_CDF_INV inverts the CDF. TRIANGLE_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 3.00000 PDF parameter C = 10.0000 X PDF CDF CDF_INV 2.98281 0.220312 0.218418 2.98281 8.34109 0.526639E-01 0.956318 8.34109 6.72267 0.104042 0.829509 6.72267 4.74517 0.166820 0.561695 4.74517 3.93076 0.192674 0.415307 3.93076 2.09093 0.121215 0.661187E-01 2.09093 3.16095 0.217113 0.257578 3.16095 2.40685 0.156316 0.109957 2.40685 1.88821 0.986903E-01 0.438290E-01 1.88821 5.19790 0.152448 0.633966 5.19790 TEST144 For the Triangle PDF: TRIANGLE_MEAN returns the mean; TRIANGLE_SAMPLE samples; TRIANGLE_VARIANCE returns the 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 = 4.67684 Sample variance = 3.70549 Sample maximum = 9.63699 Sample minimum = 1.18191 TEST145 For the Triangular PDF: TRIANGULAR_CDF evaluates the CDF; TRIANGULAR_CDF_INV inverts the CDF. TRIANGULAR_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 10.0000 X PDF CDF CDF_INV 3.97421 0.146875 0.218418 3.97421 8.66991 0.656834E-01 0.956318 8.66991 7.37229 0.129764 0.829509 7.37229 5.78677 0.208061 0.561695 5.78677 5.10121 0.202529 0.415307 5.10121 2.63640 0.808099E-01 0.661187E-01 2.63640 4.22985 0.159499 0.257578 4.22985 3.11027 0.104211 0.109957 3.11027 2.33232 0.657935E-01 0.438290E-01 2.33232 6.14975 0.190136 0.633966 6.14975 TEST146 For the Triangular PDF: TRIANGULAR_MEAN computes mean; TRIANGULAR_SAMPLE samples; TRIANGULAR_VARIANCE computes variance. PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF mean = 5.50000 PDF variance = 3.37500 Sample size = 1000 Sample mean = 5.51035 Sample variance = 3.38802 Sample maximum = 9.70895 Sample minimum = 1.27286 TEST147 For the Uniform 01 Order PDF: UNIFORM_ORDER_SAMPLE samples. Ordered sample: 1 0.174736E-01 2 0.275623E-01 3 0.131654 4 0.274807 5 0.385745 6 0.664103 7 0.768848 8 0.834884 9 0.854621 10 0.858873 TEST148 For the Uniform PDF on the N-Sphere: UNIFORM_NSPHERE_SAMPLE samples. Dimension N of sphere = 3 Points on the sphere: 1 0.915568 -0.257797 -0.308668 2 -0.171751 0.901345 0.397592 3 0.541822 0.447986 -0.711152 4 -0.620052 -0.745456 0.244603 5 0.262807E-01 -0.894727 0.445840 6 0.167158E-01 -0.591520 0.806117 7 0.987108 0.846611E-01 0.135834 8 -0.220974 0.974193 0.460176E-01 9 0.679580 -0.416543 -0.603873 10 0.936980 -0.375368E-01 0.347361 TEST1485 For the Uniform 01 PDF: UNIFORM_01_CDF evaluates the CDF; UNIFORM_01_CDF_INV inverts the CDF. UNIFORM_01_PDF evaluates the PDF; X PDF CDF CDF_INV 0.218418 1.00000 0.218418 0.218418 0.956318 1.00000 0.956318 0.956318 0.829509 1.00000 0.829509 0.829509 0.561695 1.00000 0.561695 0.561695 0.415307 1.00000 0.415307 0.415307 0.661187E-01 1.00000 0.661187E-01 0.661187E-01 0.257578 1.00000 0.257578 0.257578 0.109957 1.00000 0.109957 0.109957 0.438290E-01 1.00000 0.438290E-01 0.438290E-01 0.633966 1.00000 0.633966 0.633966 TEST1486 For the Uniform 01 PDF: UNIFORM_01_MEAN computes mean; UNIFORM_01_SAMPLE samples; UNIFORM_01_VARIANCE computes variance. PDF mean = 0.500000 PDF variance = 0.833333E-01 Sample size = 1000 Sample mean = 0.503040 Sample variance = 0.823320E-01 Sample maximum = 0.997908 Sample minimum = 0.183837E-02 TEST149 For the Uniform PDF: UNIFORM_CDF evaluates the CDF; UNIFORM_CDF_INV inverts the CDF. UNIFORM_PDF evaluates the PDF; PDF parameter A = 1.00000 PDF parameter B = 10.0000 X PDF CDF CDF_INV 2.96576 0.111111 0.218418 2.96576 9.60686 0.111111 0.956318 9.60686 8.46558 0.111111 0.829509 8.46558 6.05526 0.111111 0.561695 6.05526 4.73776 0.111111 0.415307 4.73776 1.59507 0.111111 0.661187E-01 1.59507 3.31820 0.111111 0.257578 3.31820 1.98961 0.111111 0.109957 1.98961 1.39446 0.111111 0.438290E-01 1.39446 6.70569 0.111111 0.633966 6.70569 TEST150 For the Uniform PDF: UNIFORM_MEAN computes mean; UNIFORM_SAMPLE samples; UNIFORM_VARIANCE computes variance. PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF mean = 5.50000 PDF variance = 6.75000 Sample size = 1000 Sample mean = 5.52736 Sample variance = 6.66889 Sample maximum = 9.98117 Sample minimum = 1.01655 TEST151 For the Uniform Discrete PDF: UNIFORM_DISCRETE_CDF evaluates the CDF; UNIFORM_DISCRETE_CDF_INV inverts the CDF. UNIFORM_DISCRETE_PDF evaluates the PDF; PDF parameter A = 1 PDF parameter B = 6 X PDF CDF CDF_INV 2 0.166667 0.333333 3 6 0.166667 1.00000 6 6 0.166667 1.00000 6 4 0.166667 0.666667 5 3 0.166667 0.500000 4 1 0.166667 0.166667 2 3 0.166667 0.500000 4 2 0.166667 0.333333 3 1 0.166667 0.166667 2 5 0.166667 0.833333 6 TEST152 For the Uniform discrete PDF: UNIFORM_DISCRETE_MEAN computes the mean; UNIFORM_DISCRETE_SAMPLE samples; UNIFORM_DISCRETE_VARIANCE computes the variance. PDF parameter A = 1 PDF parameter B = 6 PDF mean = 3.50000 PDF variance = 2.91667 Sample size = 1000 Sample mean = 3.94500 Sample variance = 2.70068 Sample maximum = 6 Sample minimum = 1 TEST153 For the Uniform discrete PDF. UNIFORM_DISCRETE_PDF evaluates the PDF. UNIFORM_DISCRETE_CDF evaluates the CDF. PDF parameter A = 1 PDF parameter B = 6 X PDF(X) CDF(X) 0 0.00000 0.00000 1 0.166667 0.166667 2 0.166667 0.333333 3 0.166667 0.500000 4 0.166667 0.666667 5 0.166667 0.833333 6 0.166667 1.00000 TEST154 For the Von Mises PDF: VON_MISES_CDF evaluates the CDF. VON_MISES_CDF_INV inverts the CDF. VON_MISES_PDF evaluates the PDF. PDF parameter A = 1.00000 PDF parameter B = 2.00000 X PDF CDF CDF_INV 0.476234 0.394559 0.252320 0.476235 1.12227 0.508240 0.562764 1.12227 0.931772 0.513490 0.464857 0.931774 0.575338 0.431920 0.293305 0.575339 0.862805 0.506281 0.429664 0.862805 -1.39044 0.161849E-01 0.863675E-02 -1.39042 2.77511 0.465295E-01 0.974194 2.77510 0.193915 0.278813 0.157223 0.193917 0.786199 0.492920 0.391357 0.786198 0.790531 0.493818 0.393494 0.790531 TEST155 For the Von Mises PDF: VON_MISES_MEAN computes the mean; VON_MISES_SAMPLE samples. VON_MISES_CIRCULAR_VARIANCE computes the 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 = 1.01316 Sample circular variance = 0.307398 Sample maximum = 4.09050 Sample minimum = -2.04316 TEST1555: VON_MISES_CDF evaluates the cumulative distribution function for the von Mises PDF. VON_MISES_CDF_VALUES returns some exact values. A is the dominant angle; B is a measure of spread; X is the angle; A B X Exact F Computed F 0.0000 1.0000 -2.6180 0.2535089956281180E-01 0.2535089696295341E-01 0.0000 1.0000 -1.5708 0.1097539041177346 0.1097539045228035 0.0000 1.0000 0.0000 0.5000000000000000 0.5000000000000000 0.0000 1.0000 1.0472 0.8043381312498558 0.8043381287630230 0.0000 1.0000 2.0944 0.9417460124555197 0.9417460153778769 1.0000 2.0000 1.0000 0.5000000000000000 0.5000000000000000 1.0000 2.0000 1.2000 0.6018204118446155 0.6018204081541774 1.0000 2.0000 1.4000 0.6959356933122230 0.6959356966369082 1.0000 2.0000 1.6000 0.7765935901304593 0.7765935908423945 1.0000 2.0000 1.8000 0.8410725934916615 0.8410725895214860 1.0000 2.0000 2.0000 0.8895777369550366 0.8895777397545719 -2.0000 3.0000 0.0000 0.9960322705517926 0.9960322719470017 -1.0000 3.0000 0.0000 0.9404336090170247 0.9404336096280537 0.0000 3.0000 0.0000 0.5000000000000000 0.5000000000000000 1.0000 3.0000 0.0000 0.5956639098297530E-01 0.5956639037194624E-01 2.0000 3.0000 0.0000 0.3967729448207649E-02 0.3967728052998318E-02 3.0000 3.0000 0.0000 0.2321953958111930E-03 0.2321935194129232E-03 0.0000 0.0000 0.7854 0.6250000000000000 0.6250000000000000 0.0000 1.0000 0.7854 0.7438406999109122 0.7438406996376531 0.0000 2.0000 0.7854 0.8369224904294019 0.8369224863303987 0.0000 3.0000 0.7854 0.8941711407897124 0.8941711410833787 0.0000 4.0000 0.7854 0.9291058600568743 0.9291058631988147 0.0000 5.0000 0.7854 0.9514289900655436 0.9514289952795482 TEST156 For the Weibull PDF: WEIBULL_CDF evaluates the CDF; WEIBULL_CDF_INV inverts the CDF. WEIBULL_PDF evaluates the PDF; PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4.00000 X PDF CDF CDF_INV 4.11372 0.364494 0.218418 4.11372 5.99057 0.137084 0.956318 5.99057 5.45985 0.348698 0.829509 5.45985 4.85900 0.505816 0.561695 4.85900 4.56772 0.488817 0.415307 4.56772 3.53425 0.166552 0.661187E-01 3.53425 4.21624 0.399093 0.257578 4.21624 3.75263 0.236621 0.109957 3.75263 3.38034 0.124184 0.438290E-01 3.38034 5.00376 0.489885 0.633966 5.00376 TEST157 For the Weibull PDF: WEIBULL_MEAN computes the mean; WEIBULL_SAMPLE samples; WEIBULL_VARIANCE computes the 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 = 4.72250 Sample variance = 0.587748 Sample maximum = 6.72812 Sample minimum = 2.62134 TEST158 For the Weibull Discrete PDF, WEIBULL_DISCRETE_CDF evaluates the CDF; WEIBULL_DISCRETE_CDF_INV inverts the CDF. WEIBULL_DISCRETE_PDF evaluates the PDF; PDF parameter A = 0.500000 PDF parameter B = 1.50000 X PDF CDF CDF_INV 0 0.500000 0.500000 0 2 0.113508 0.972723 2 1 0.359214 0.859214 1 1 0.359214 0.859214 1 0 0.500000 0.500000 0 0 0.500000 0.500000 0 0 0.500000 0.500000 0 0 0.500000 0.500000 0 0 0.500000 0.500000 0 1 0.359214 0.859214 1 TEST159 For the Weibull Discrete PDF: WEIBULL_DISCRETE_PDF evaluates the PDF; WEIBULL_DISCRETE_CDF evaluates the CDF. PDF parameter A = 0.500000 PDF parameter B = 1.50000 X PDF(X) CDF(X) 0 0.500000 0.500000 1 0.359214 0.859214 2 0.113508 0.972723 3 0.233711E-01 0.996094 4 0.347534E-02 0.999569 5 0.393254E-03 0.999962 6 0.349916E-04 0.999997 7 0.250545E-05 1.00000 8 0.146886E-06 1.00000 9 0.714817E-08 1.00000 10 0.291997E-09 1.00000 TEST160 For the discrete Weibull PDF: WEIBULL_DISCRETE_SAMPLE samples. PDF parameter A = 0.500000 PDF parameter B = 1.50000 Sample size = 1000 Sample mean = 0.676000 Sample variance = 0.621646 Sample maximum = 4 Sample minimum = 0 TEST161 For the Zipf PDF: ZIPF_PDF evaluates the PDF. ZIPF_CDF evaluates the CDF. PDF parameter A = 2.00000 X PDF(X) CDF(X) 1 0.607927 0.607927 2 0.151982 0.759909 3 0.675475E-01 0.827456 4 0.379954E-01 0.865452 5 0.243171E-01 0.889769 6 0.168869E-01 0.906656 7 0.124067E-01 0.919062 8 0.949886E-02 0.928561 9 0.750527E-02 0.936067 10 0.607927E-02 0.942146 11 0.502419E-02 0.947170 12 0.422172E-02 0.951392 13 0.359720E-02 0.954989 14 0.310167E-02 0.958091 15 0.270190E-02 0.960792 16 0.237472E-02 0.963167 17 0.210355E-02 0.965271 18 0.187632E-02 0.967147 19 0.168401E-02 0.968831 20 0.151982E-02 0.970351 TEST162 For the Zipf PDF: ZIPF_SAMPLE samples. PDF parameter A = 4.00000 PDF mean = 1.11063 PDF variance = 0.286326 Sample size = 1000 Sample mean = 1.12000 Sample variance = 0.197798 Sample maximum = 6 Sample minimum = 1 prob_test(): Normal end of execution. 1 November 2024 2:58:02.704 PM