15 July 2022 12:42:19.469 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 9 2.222222 0.919370 100 61 3.278689 0.137096 10000 6297 3.176116 0.345230E-01 1000000 636322 3.143063 0.147014E-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 TEST029 For the Cauchy PDF: CAUCHY_MEAN computes the mean; CAUCHY_VARIANCE computes the variance; CAUCHY_SAMPLE samples. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF mean = 2.00000 PDF mean = 0.100000E+31 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: 1 2.12288 2 1.00000 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 14 0.871784E+11 I4_FACTORIAL - Fatal error! I4_FACTORIAL(N) cannot be computed as an integer for 13 < N. Input value N = 14