June 24 2002 1:39:23.565 PM PROB_PRB Sample problems for the PROB routines. TEST201 For the Anglit PDF: ANGLIT_CDF evaluates the CDF; ANGLIT_CDF_INV inverts the CDF. ANGLIT_PDF evaluates the PDF; PDF argument X = 0.500000 PDF value = 0.977061 CDF value = 0.920735 CDF_INV value X = 0.500000 TEST202 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 = -0.693936E-02 Sample variance = 0.115112 Sample maximum = 0.721451 Sample minimum = -0.762128 TEST001 For the Arcsin PDF: ARCSIN_CDF evaluates the CDF; ARCSIN_CDF_INV inverts the CDF. ARCSIN_PDF evaluates the PDF; PDF argument X = 0.500000 PDF value = 0.636620 CDF value = 0.333333 CDF_INV value X = 0.500000 TEST003 For the Arcsin PDF: ARCSIN_MEAN computes the mean; ARCSIN_SAMPLE samples; ARCSIN_VARIANCE computes the variance. PDF mean = 0.500000 PDF variance = 0.125000 Sample size = 1000 Sample mean = 0.637873 Sample variance = 0.974452E-01 Sample maximum = 0.999993 Sample minimum = 0.557919E-02 TEST004 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 0.791813E-01 6 0.669468E-01 7 0.579920E-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 TEST005 For the Bernoulli PDF, BERNOULLI_CDF evaluates the CDF; BERNOULLI_CDF_INV inverts the CDF. CDF_INV argument CDF = 0.500000 PDF parameter A = 0.750000 CDF_INV value X = 1 (Expected answer is 0) PDF argument X = 1 CDF value = 1.00000 (Expected answer is 0.75) TEST006 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 = 0.766000 Sample variance = 0.179422 Sample maximum = 1 Sample minimum = 0 TEST007 For the Bernoulli PDF: BERNOULLI_PDF evaluates the PDF. BERNOULLI_CDF evaluates the CDF. PDF parameter A = 0.750000 X PDF(X) CDF(X) 0 0.250000 0.250000 1 0.750000 1.00000 TEST008 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 TEST009 For the Beta PDF: BETA_CDF evaluates the CDF; BETA_CDF_INV inverts the CDF. BETA_PDF evaluates the PDF; PDF argument X = 0.600000 PDF parameter A = 12.0000 PDF parameter B = 12.0000 PDF value = 2.46892 CDF value = 0.836356 CDF_INV value X = 0.599998 TEST010: BETA_INC evaluates the normalized incomplete Beta function BETA_INC(A,B,X). A B X Exact F BETA_INC(A,B,X) 0.5000 0.5000 0.0100 0.637686E-01 0.637686E-01 0.5000 0.5000 0.1000 0.204833 0.204833 0.5000 0.5000 1.0000 1.00000 1.00000 1.0000 0.5000 0.0100 0.501260E-02 0.501256E-02 1.0000 0.5000 0.1000 0.513167E-01 0.513167E-01 1.0000 0.5000 1.0000 1.00000 1.00000 1.0000 1.0000 0.5000 0.500000 0.500000 5.0000 5.0000 0.5000 0.500000 0.500000 10.0000 0.5000 0.9000 0.151641 0.151641 10.0000 5.0000 0.5000 0.897827E-01 0.897828E-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 0.459876 20.0000 10.0000 0.6000 0.214682 0.214680 20.0000 10.0000 0.8000 0.950737 0.950737 20.0000 20.0000 0.5000 0.500000 0.499998 20.0000 20.0000 0.6000 0.897941 0.897942 30.0000 10.0000 0.7000 0.224130 0.224131 30.0000 10.0000 0.8000 0.758641 0.758639 40.0000 20.0000 0.7000 0.700178 0.700180 TEST011 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 = 0.399745 Sample variance = 0.382146E-01 Sample maximum = 0.953588 Sample minimum = 0.172333E-01 TEST013 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 argument X = 2 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4 PDF value = 0.257143 CDF value = 0.757142 CDF_INV value = 2 TEST014 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 = 1.60800 Sample variance = 1.45780 Sample maximum = 4 Sample minimum = 0 TEST015 For the Beta Binomial PDF: BETA_BINOMIAL_PDF evaluates the PDF; BETA_BINOMIAL_CDF evaluates the CDF. PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4 X PDF(X) CDF(X) 0 0.214285 0.214285 1 0.285714 0.499999 2 0.257143 0.757142 3 0.171428 0.928570 4 0.714284E-01 1.00000 TEST016 For the Beta Pascal PDF: BETA_PASCAL_CDF evaluates the CDF; BETA_PASCAL_CDF_INV inverts the CDF. BETA_PASCAL_PDF evaluates the PDF; PDF argument X = 7 PDF parameter A = 5 PDF parameter B = 3.00000 PDF parameter C = 4.00000 PDF value = 0.178571E-01 CDF value = 0.101190 CDF_INV value = 7 TEST017 For the Beta Pascal PDF: BETA_PASCAL_MEAN computes the mean; BETA_PASCAL_SAMPLE samples; BETA_PASCAL_VARIANCE computes the variance. PDF parameter A = 5 PDF parameter B = 3.00000 PDF parameter C = 4.00000 PDF mean = 7.50000 PDF variance = 26.2500 TEST017 - DEBUG - BETA_PASCAL_SAMPLE is still goofy! TEST018 For the Beta Pascal PDF: BETA_PASCAL_PDF evaluates the PDF; BETA_PASCAL_CDF evaluates the CDF. PDF parameter A = 5 PDF parameter B = 3.00000 PDF parameter C = 4.00000 X PDF(X) CDF(X) 5 0.535714E-01 0.535714E-01 6 0.297619E-01 0.833333E-01 7 0.178571E-01 0.101190 8 0.113636E-01 0.112554 9 0.757575E-02 0.120130 10 0.524475E-02 0.125375 11 0.374624E-02 0.129121 12 0.274725E-02 0.131868 13 0.206044E-02 0.133928 14 0.157563E-02 0.135504 15 0.122549E-02 0.136730 TEST0185: BINOMIAL_CDF evaluates the cumulative distribution function for the discrete binomial probability density function. 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) 0.0000 0.0500 0.0000 0.902500 0.902500 0.0000 0.0500 0.0000 0.997500 0.997500 0.0000 0.0500 0.0000 1.00000 1.00000 0.0000 0.5000 0.0000 0.250000 0.250000 0.0000 0.5000 0.0000 0.750000 0.750000 0.0000 0.2500 0.0000 0.316400 0.316406 0.0000 0.2500 0.0000 0.738300 0.738281 0.0000 0.2500 0.0000 0.949200 0.949219 0.0000 0.2500 0.0000 0.996100 0.996094 0.0000 0.0500 0.0000 0.999900 0.999936 0.0000 0.1000 0.0000 0.998400 0.998365 0.0000 0.1500 0.0000 0.990100 0.990126 0.0000 0.2000 0.0000 0.967200 0.967207 0.0000 0.2500 0.0000 0.921900 0.921873 0.0000 0.3000 0.0000 0.849700 0.849732 0.0000 0.4000 0.0000 0.633100 0.633103 0.0000 0.5000 0.0000 0.377000 0.376953 TEST019 For the Binomial PDF: BINOMIAL_CDF evaluates the CDF; BINOMIAL_CDF_INV inverts the CDF. BINOMIAL_PDF evaluates the PDF; PDF argument X = 3 PDF parameter A = 5 PDF parameter B = 0.950000 PDF value = 0.214344E-01 CDF value = 0.225925E-01 CDF_INV value X = 3 TEST020 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 TEST021 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 = 1.54600 Sample variance = 1.06094 Sample maximum = 5 Sample minimum = 0 TEST022 For the Binomial PDF: BINOMIAL_PDF evaluates the PDF. BINOMIAL_CDF evaluates the CDF. PDF parameter A = 5 PDF parameter B = 0.950000 X PDF(X) CDF(X) -1 0.00000 0.00000 0 0.312500E-06 0.312500E-06 1 0.296875E-04 0.300000E-04 2 0.112813E-02 0.115813E-02 3 0.214344E-01 0.225925E-01 4 0.203627 0.226219 5 0.773781 1.00000 6 0.00000 1.00000 TEST220 For the Bradford PDF: BRADFORD_CDF evaluates the CDF; BRADFORD_CDF_INV inverts the CDF. BRADFORD_PDF evaluates the PDF; PDF argument X = 1.25000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF value = 1.23660 CDF value = 0.403677 CDF_INV value X = 1.25000 TEST221 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 = 1.39075 Sample variance = 0.821657E-01 Sample maximum = 1.99757 Sample minimum = 1.00001 TEST023 For the Burr PDF: BURR_CDF evaluates the CDF; BURR_CDF_INV inverts the CDF. BURR_PDF evaluates the PDF; PDF argument X = 3.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF parameter D = 2.00000 PDF value = 0.375000 CDF value = 0.250000 CDF_INV value X = 3.00000 TEST024 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 = 5.72506 Sample size = 1000 Sample mean = 4.25069 Sample variance = 5.80844 Sample maximum = 27.4857 Sample minimum = 1.61215 TEST026 For the Cauchy PDF: CAUCHY_CDF evaluates the CDF; CAUCHY_CDF_INV inverts the CDF. CAUCHY_PDF evaluates the PDF; PDF argument X = 0.750000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF value = 0.904075E-01 CDF value = 0.374334 CDF_INV value X = 0.750000 TEST027 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 = 0.340282E+39 Sample size = 1000 Sample mean = 2.86397 Sample variance = 4226.32 Sample maximum = 1246.93 Sample minimum = -792.582 TEST028 For the Chi PDF: CHI_CDF evaluates the CDF. CHI_CDF_INV inverts the CDF. CHI_PDF evaluates the PDF. PDF argument X = 2.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF value = 0.880163E-01 CDF value = 0.308596E-01 CDF_INV value = 2.00000 TEST527 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 = 1.81409 Sample size = 1000 Sample mean = 4.28258 Sample variance = 1.72336 Sample maximum = 8.77677 Sample minimum = 1.47197 TEST0295: CHISQUARE_CENTRAL_CDF evaluates the cumulative distribution function for the chi-square central probability density function. A X Exact F CHISQUARE_CENTRAL_CDF(A,X) 1 0.0100 0.920340 0.920344 2 0.0100 0.995010 0.995012 1 0.0200 0.887540 0.887537 2 0.0200 0.990050 0.990050 1 0.4000 0.527090 0.527089 2 0.4000 0.818730 0.818731 3 0.4000 0.940240 0.940243 4 0.4000 0.982480 0.982477 1 1.0000 0.317310 0.317310 2 1.0000 0.606530 0.606531 3 1.0000 0.801250 0.801252 4 1.0000 0.909800 0.909796 5 1.0000 0.962570 0.962566 3 2.0000 0.572410 0.572407 3 3.0000 0.391630 0.391625 3 4.0000 0.261460 0.261464 3 5.0000 0.171800 0.171797 3 6.0000 0.111610 0.111610 TEST030 For the central chi square PDF: CHISQUARE_CENTRAL_CDF evaluates the CDF; CHISQUARE_CENTRAL_CDF_INV inverts the CDF. CHISQUARE_CENTRAL_PDF evaluates the PDF; PDF argument X = 6.00000 PDF parameter A = 4.00000 PDF value = 0.746806E-01 CDF value = 0.199148 CDF_INV value X = -201.426 TEST031 For the central chi square PDF: CHISQUARE_CENTRAL_MEAN computes the mean; CHISQUARE_CENTRAL_SAMPLE samples; CHISQUARE_CENTRAL_VARIANCE computes the variance. PDF parameter A = 10.0000 PDF mean = 10.0000 PDF variance = 20.0000 Sample size = 1000 Sample mean = 9.99370 Sample variance = 20.8377 Sample maximum = 32.8567 Sample minimum = 1.45207 TEST033 For the noncentral chi square PDF: CHISQUARE_NONCENTRAL_SAMPLE samples. PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF mean = 5.00000 PDF variance = 14.0000 Sample size = 1000 Sample mean = 5.01461 Sample variance = 14.4348 Sample maximum = 21.1932 Sample minimum = 0.123483 TEST909 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 = 9.99522 4.06207 Sample variance = 2.18139 2.29816 Sample maximum = 12.9014 6.98109 Sample minimum = 7.05934 1.00313 TEST034 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 = 0.271911E-02 -0.130793E-01 Sample variance = 0.959627 1.01084 Sample maximum = 2.99137 3.10067 Sample minimum = -2.63651 -3.25827 TEST224 For the Cosine PDF: COSINE_CDF evaluates the CDF. COSINE_CDF_INV inverts the CDF. COSINE_PDF evaluates the PDF. PDF argument X = 1.00000 PDF parameter A = 2.00000 PDF parameter B = 1.00000 PDF value 0.859918E-01 CDF value 0.206921 CDF_INV value 0.999844 TEST225 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 = 2.00159 Sample variance = 1.25886 Sample maximum = 4.79798 Sample minimum = -0.773437 TEST226 COUPON_SIMULATE simulates the coupon collector's problem. Number of coupon types is 5 Expected wait is about 8.04719 1 12 2 11 3 12 4 17 5 7 6 8 7 16 8 12 9 7 10 12 Average wait was 11.4000 Number of coupon types is 10 Expected wait is about 23.0259 1 71 2 38 3 26 4 19 5 33 6 35 7 38 8 25 9 24 10 23 Average wait was 33.2000 Number of coupon types is 15 Expected wait is about 40.6208 1 47 2 71 3 70 4 56 5 66 6 38 7 35 8 41 9 40 10 50 Average wait was 51.4000 Number of coupon types is 20 Expected wait is about 59.9146 1 38 2 72 3 74 4 61 5 62 6 92 7 50 8 62 9 119 10 56 Average wait was 68.6000 Number of coupon types is 25 Expected wait is about 80.4719 1 104 2 184 3 75 4 72 5 74 6 102 7 123 8 76 9 80 10 73 Average wait was 96.3000 TEST035 For the Deranged PDF: DERANGED_CDF evaluates the CDF; DERANGED_CDF_INV inverts the CDF. DERANGED_PDF evaluates the PDF; PDF argument X = 3 PDF parameter A = 7 PDF value = 0.625000E-01 CDF value = 0.981746 CDF_INV value X = 3 TEST036 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 TEST037 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 = 0.979000 Sample variance = 1.05961 Sample maximum = 5 Sample minimum = 0 TEST038 For the Dipole PDF: DIPOLE_CDF evaluates the CDF. DIPOLE_CDF_INV inverts the CDF. DIPOLE_PDF evaluates the PDF. PDF argument X = 0.600000 PDF parameter A = 0.00000 PDF parameter B = 1.00000 PDF value = 0.536674 CDF value = 0.812452 CDF_INV value = 0.600098 PDF argument X = 0.600000 PDF parameter A = 0.785398 PDF parameter B = 0.500000 PDF value = 0.282172 CDF value = 0.613508 CDF_INV value = 0.600098 PDF argument X = 0.600000 PDF parameter A = 1.57080 PDF parameter B = 0.00000 PDF value = 0.234051 CDF value = 0.672021 CDF_INV value = 0.599609 TEST040 For the Dipole PDF: DIPOLE_SAMPLE samples. PDF parameter A = 0.00000 PDF parameter B = 1.00000 Sample size = 1000 Sample mean = 0.350147E-01 Sample variance = 0.730021 Sample maximum = 7.01114 Sample minimum = -5.23047 PDF parameter A = 0.785398 PDF parameter B = 0.500000 Sample size = 1000 Sample mean = -0.709715 Sample variance = 464.562 Sample maximum = 115.977 Sample minimum = -341.986 PDF parameter A = 1.57080 PDF parameter B = 0.00000 Sample size = 1000 Sample mean = -4.23611 Sample variance = 7066.50 Sample maximum = 375.288 Sample minimum = -2459.09 TEST041 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(I), I = 1 to N: 1 0.250000 2 0.500000 3 1.25000 PDF mean, variance: 1 0.125000 0.364583E-01 2 0.250000 0.625000E-01 3 0.625000 0.781250E-01 Second moments: 0.520833E-01 0.208333E-01 0.520833E-01 0.208333E-01 0.125000 0.104167 0.520833E-01 0.104167 0.468750 Sample size = 1000 Observed Min, Max, Mean, Variance: 1 0.957726E-12 0.920417 0.124518 0.354507E-01 2 0.607911E-06 0.994453 0.257302 0.610334E-01 3 0.393866E-02 0.999988 0.618180 0.773083E-01 TEST042 For the Dirichlet PDF: DIRICHLET_PDF evaluates the PDF. Number of components N = 3 PDF arguments X(I), I = 1 to N: 1 0.500000 2 0.125000 3 0.375000 PDF parameters A(I), I = 1 to N: 1 0.250000 2 0.500000 3 1.25000 PDF value = 0.639070 TEST043 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): 0.250000 2.00000 0.500000 0.00000 1.25000 2.00000 Component weights: 1 1.00000 2 2.00000 PDF mean: 1 0.375000 2 0.833333E-01 3 0.541667 Sample size = 1000 Observed Min, Max, Mean, Variance: 1 0.598594E-11 0.991960 0.378671 0.769353E-01 2 0.00000 0.994133 0.762717E-01 0.296219E-01 3 0.584862E-02 0.999905 0.545058 0.626413E-01 TEST044 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): 0.250000 2.00000 0.500000 0.00000 1.25000 2.00000 Component weights: 1 1.00000 2 2.00000 PDF value = 0.213023 TEST045 BETA_PDF evaluates the Beta PDF. DIRICHLET_PDF evaluates the Dirichlet PDF. For N = 2, Dirichlet = Beta. Number of components N = 2 PDF arguments X(I), I = 1 to N: 1 0.250000 2 0.750000 PDF parameters A(I), I = 1 to N: 1 2.50000 2 3.50000 Dirichlet PDF value = 1.65399 Beta PDF value = 1.65399 TEST046 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(CDF) 0 0.00000 0.00000 1 1 0.625000E-01 0.625000E-01 1 2 0.125000 0.187500 2 3 0.375000 0.562500 3 4 0.125000 0.687500 4 5 0.250000 0.937500 5 6 0.625000E-01 1.00000 6 7 0.00000 1.00000 6 TEST047 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 = 3.58900 Sample variance = 1.69778 Sample maximum = 6 Sample minimum = 1 TEST0481 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 argument X = 4.50000 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 value = 0.200000 CDF value = 0.700000 CDF_INV value X2 = 4.50000 TEST0482 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 = 4.23000 Sample variance = 11.2974 Sample maximum = 10.0000 Sample minimum = 0.00000 TEST0483 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 TEST049 For the Erlang PDF: ERLANG_CDF evaluates the CDF. ERLANG_CDF_INV inverts the CDF. ERLANG_PDF evaluates the PDF. PDF argument X = 4.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3 PDF value 0.125511 CDF value 0.191153 CDF_INV 4.00000 TEST050 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 = 7.08033 Sample variance = 12.5327 Sample maximum = 23.2496 Sample minimum = 1.43421 TEST052 ERROR_FUNCTION evaluates ERF(X). ERF argument X = 1.00000 ERF value 0.842701 (Expected answer is 0.843) Test: 0.5 * ( ERF(X/SQRT(2)) + 1 ) = Normal_CDF(X) 0.5 * ( ERF(X/SQRT(2)) + 1 ) = 0.841345 Normal_CDF(X) = 0.841345 TEST053 For the Exponential 01 PDF: EXPONENTIAL_01_CDF evaluates the CDF. EXPONENTIAL_01_CDF_INV inverts the CDF. EXPONENTIAL_01_PDF evaluates the PDF. PDF argument X = 0.500000 PDF value 0.606531 CDF value 0.393469 CDF_INV value X 0.500000 TEST054 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 = 1.00171 Sample variance = 0.941685 Sample maximum = 5.63130 Sample minimum = 0.105096E-02 TEST056 For the Exponential CDF: EXPONENTIAL_CDF evaluates the CDF. EXPONENTIAL_CDF_INV inverts the CDF. EXPONENTIAL_PDF evaluates the PDF. PDF argument X = 2.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF value 0.303265 CDF value 0.393469 CDF_INV value X 2.00000 TEST057 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 = 11.3374 Sample variance = 105.612 Sample maximum = 80.2179 Sample minimum = 1.00057 TEST059 For the Extreme CDF: EXTREME_CDF evaluates the CDF; EXTREME_CDF_INV inverts the CDF. EXTREME_PDF evaluates the PDF; PDF argument X = 1.90000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF value = 0.122558 CDF value = 0.355619 CDF_INV value X = 1.90000 TEST060 For the Extreme PDF: EXTREME_MEAN computes the mean; EXTREME_SAMPLE samples; EXTREME_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 = 3.85114 Sample variance = 14.1925 Sample maximum = 20.3255 Sample minimum = -3.15821 TEST061: F_CENTRAL_CDF evaluates the F central CDF. A B X Exact F F_CENTRAL_CDF(A,B,X) 1 1 1.0000 0.500000 0.500000 1 5 0.5280 0.500000 0.500029 5 1 1.8900 0.500000 0.500397 1 5 1.6900 0.250000 0.250301 2 10 1.6000 0.250000 0.249534 4 20 1.4700 0.250000 0.248584 1 5 4.0600 0.100000 0.100013 6 6 3.0500 0.100000 0.100287 8 16 2.0900 0.100000 0.997154E-01 1 5 6.6100 0.500000E-01 0.499751E-01 3 10 3.7100 0.500000E-01 0.499425E-01 6 12 3.0000 0.500000E-01 0.498074E-01 1 5 10.0100 0.250000E-01 0.249866E-01 1 5 16.2600 0.100000E-01 0.999777E-02 1 5 22.7800 0.500000E-02 0.500221E-02 1 5 47.1800 0.100000E-02 0.100004E-02 TEST062 For the central F PDF: F_CENTRAL_CDF evaluates the CDF. F_CENTRAL_PDF evaluates the PDF. PDF argument X = 648.000 PDF parameter M = 1 PDF parameter N = 1 PDF value = 0.192672E-04 CDF value = 0.249959E-01 TEST063 For the central F PDF: F_CENTRAL_MEAN computes the mean; F_CENTRAL_SAMPLE samples; F_CENTRAL_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 = 1.52507 Sample variance = 7.16066 Sample maximum = 70.6473 Sample minimum = 0.994612E-01 TEST0645 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 TEST065 FACTORIAL_STIRLING computes Stirling's approximate factorial function; I_FACTORIAL evaluates the factorial function; R_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 10 0.362881E+07 0.362880E+07 11 0.399169E+08 0.399168E+08 12 0.479003E+09 0.479002E+09 13 0.622703E+10 0.622702E+10 14 0.871785E+11 0.871783E+11 15 0.130768E+13 0.130767E+13 16 0.209228E+14 0.209228E+14 17 0.355688E+15 0.355687E+15 18 0.640238E+16 0.640237E+16 19 0.121645E+18 0.121645E+18 20 0.243291E+19 0.243290E+19 TEST066 For the Fisk PDF: FISK_CDF evaluates the CDF; FISK_CDF_INV inverts the CDF. FISK_PDF evaluates the PDF; PDF argument X = 1.90000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF value = 0.255133 CDF value = 0.835147E-01 CDF_INV value X = 1.90000 TEST067 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 = 3.43256 Sample variance = 3.41209 Sample maximum = 20.6754 Sample minimum = 1.19756 TEST069 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 argument X = 0.500000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF value 0.211326 CDF value 0.106209 CDF_INV value X = 0.499914 TEST070 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 = 2.79982 Sample variance = 4.14547 Sample maximum = 10.9932 Sample minimum = 0.195493E-02 TEST072 GAMMA evaluates the Gamma function; GAMMA_LOG evaluates the log of the Gamma function; GAMMA_LOG_INT evaluates the log for integer argument; R_FACTORIAL evaluates the factorial function. X, GAMMA(X), Exp(GAMMA_LOG(X)), Exp(GAMMA_LOG_INT(X)) R_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. TEST073: GAMMA_INC evaluates the normalized incomplete Gamma function P(A,X). A X Exact F GAMMA_INC(A,X) 0.1000 0.0316 0.742026 0.742026 0.1000 0.3162 0.911975 0.911975 0.1000 1.5811 0.989896 0.989896 0.5000 0.0707 0.293128 0.293128 0.5000 0.7071 0.765642 0.765642 0.5000 3.5355 0.992166 0.992166 1.0000 0.1000 0.951626E-01 0.951626E-01 1.0000 1.0000 0.632121 0.632120 1.0000 5.0000 0.993262 0.993262 1.1000 0.1049 0.757471E-01 0.757471E-01 1.1000 1.0488 0.607646 0.607646 1.1000 5.2440 0.993343 0.993342 2.0000 0.1414 0.910540E-02 0.910536E-02 2.0000 1.4142 0.413064 0.413064 2.0000 7.0711 0.993145 0.993145 6.0000 2.4495 0.387318E-01 0.387318E-01 6.0000 12.2474 0.982594 0.982594 11.0000 16.5831 0.940427 0.940427 26.0000 25.4951 0.486387 0.486388 41.0000 44.8219 0.735971 0.735968 TEST074 For the Gamma PDF: GAMMA_CDF evaluates the CDF. GAMMA_PDF evaluates the PDF. PDF parameter A = 1.00000 PDF parameter B = 1.50000 PDF parameter C = 3.00000 X PDF CDF 0.00000 0.00000 0.00000 0.200000 0.00000 0.00000 0.400000 0.00000 0.00000 0.600000 0.00000 0.00000 0.800000 0.00000 0.00000 1.00000 0.00000 0.00000 1.20000 0.518622E-02 0.357587E-03 1.40000 0.181553E-01 0.259110E-02 1.60000 0.357504E-01 0.792633E-02 1.80000 0.556227E-01 0.170417E-01 2.00000 0.760618E-01 0.302121E-01 TEST075 For the Gamma PDF: GAMMA_MEAN computes the mean; GAMMA_SAMPLE samples; GAMMA_VARIANCE computes the variance. TEST NUMBER: 1 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 = 7.00359 Sample variance = 19.0186 Sample maximum = 27.7476 Sample minimum = 1.03472 TEST NUMBER: 2 PDF parameter A = 2.00000 PDF parameter B = 0.500000 PDF parameter C = 0.500000 PDF mean = 2.25000 PDF variance = 0.125000 Sample size = 1000 Sample mean = 2.24631 Sample variance = 0.130699 Sample maximum = 5.53586 Sample minimum = 2.00000 TEST620 For the Generalized Logistic PDF: GENLOGISTIC_PDF evaluates the PDF. GENLOGISTIC_CDF evaluates the CDF; GENLOGISTIC_CDF_INV inverts the CDF. PDF argument X = 1.25000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF value 0.105407 CDF value = 0.149898 CDF_INV value X = 1.25000 TEST621 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 = 4.02569 Sample variance = 8.55210 Sample maximum = 18.1056 Sample minimum = -5.90100 TEST077 For the Geometric PDF: GEOMETRIC_CDF evaluates the CDF; GEOMETRIC_CDF_INV inverts the CDF. GEOMETRIC_PDF evaluates the PDF; PDF argument X = 5 PDF parameter A = 0.250000 PDF value = 0.791016E-01 CDF value = 0.762695 CDF_INV value X = 6 TEST078 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 = 3.94500 Sample variance = 11.3413 Sample maximum = 26 Sample minimum = 1 TEST079 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 TEST0795 For the Gompertz PDF: GOMPERTZ_CDF evaluates the CDF; GOMPERTZ_CDF_INV inverts the CDF. GOMPERTZ_PDF evaluates the PDF; PDF argument X = 0.600000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF value = 0.487939 CDF value = 0.892693 CDF_INV value X = 0.600000 TEST0796 For the Gompertz PDF: GOMPERTZ_SAMPLE samples; PDF parameter A = 2.00000 PDF parameter B = 3.00000 Sample size = 1000 Sample mean = 0.276903 Sample variance = 0.583661E-01 Sample maximum = 1.33211 Sample minimum = 0.288928E-04 TEST456 For the Gumbel PDF: GUMBEL_CDF evaluates the CDF. GUMBEL_CDF_INV inverts the CDF. GUMBEL_PDF evaluates the PDF. PDF argument X = 0.500000 PDF value 0.330704 CDF value 0.545239 CDF_INV value X 0.500000 TEST457 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 = 0.568830 Sample variance = 1.66601 Sample maximum = 7.93484 Sample minimum = -2.06055 TEST080 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 argument X = 0.500000 PDF parameter A = 0.00000 PDF parameter B = 2.00000 PDF value 0.386668 CDF value 0.197413 CDF_INV value X 0.500000 TEST081 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 = 7.89760 Sample variance = 37.9481 Sample maximum = 41.4585 Sample minimum = 0.767652E-02 TEST083 For the Hypergeometric PDF: HYPERGEOMETRIC_CDF evaluates the CDF. HYPERGEOMETRIC_PDF evaluates the PDF. PDF argument X = 7 Total number of balls = 1000 Number of white balls = 70 Number of balls taken = 100 PDF value = = 0.162813 CDF value = = 0.599335 TEST085 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! TEST086 I_ROUNDUP rounds reals up. -1.20000 -1 -1.00000 -1 -0.800000 0 -0.600000 0 -0.400000 0 -0.200000 0 0.00000 0 0.200000 1 0.400000 1 0.600000 1 0.800000 1 1.00000 1 1.20000 2 TEST087 For the Inverse Gaussian PDF: INVERSE_GAUSSIAN_CDF evaluates the CDF. INVERSE_GAUSSIAN_PDF evaluates the PDF. PDF argument X = 1.00000 PDF parameter A = 5.00000 PDF parameter B = 2.00000 PDF value = 0.297493 CDF value = 0.228749 TEST088 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 = 1.94729 Sample variance = 2.37288 Sample maximum = 13.5433 Sample minimum = 0.177148 TEST089 For the Laplace PDF: LAPLACE_CDF evaluates the CDF; LAPLACE_CDF_INV inverts the CDF. LAPLACE_PDF evaluates the PDF; PDF argument X = 3.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF value = 0.919699E-01 CDF value = 0.816060 CDF_INV value X = 3.00000 TEST090 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 = 0.990195 Sample variance = 7.85257 Sample maximum = 11.4125 Sample minimum = -13.2927 TEST092 For the Logistic PDF: LOGISTIC_CDF evaluates the CDF; LOGISTIC_CDF_INV inverts the CDF. LOGISTIC_PDF evaluates the PDF; PDF argument X = 3.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF value = 0.983060E-01 CDF value = 0.731059 CDF_INV value X = 3.00000 TEST093 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 = 2.16094 Sample variance = 28.7687 Sample maximum = 21.6630 Sample minimum = -21.1241 TEST095 For the Lognormal PDF: LOGNORMAL_CDF evaluates the CDF; LOGNORMAL_CDF_INV inverts the CDF. LOGNORMAL_PDF evaluates the PDF; PDF argument X = 8103.08 PDF parameter A = 10.0000 PDF parameter B = 2.25000 PDF value = 0.198237E-04 CDF value = 0.328361 CDF_INV value X = 8103.08 TEST096 For the Lognormal PDF: LOGNORMAL_MEAN computes the mean; LOGNORMAL_SAMPLE samples; LOGNORMAL_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 = 23.2037 Sample variance = 19045.3 Sample maximum = 2729.56 Sample minimum = 0.546637E-02 TEST098 For the Logseries PDF, LOGSERIES_CDF evaluates the CDF; LOGSERIES_CDF_INV inverts the CDF. LOGSERIES_PDF evaluates the PDF; PDF argument = 3 PDF parameter A = 0.250000 PDF value = 0.181045E-01 CDF value = 0.995746 CDF_INV value = 4 TEST099 For the Logseries PDF: LOGSERIES_CDF evaluates the CDF; LOGSERIES_PDF evaluates the PDF. PDF argument X = 2 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 TEST100 For the Logseries PDF: LOGSERIES_MEAN computes the mean; LOGSERIES_VARIANCE computes the variance; LOGSERIES_SAMPLE samples. PDF parameter A = 0.250000 PDF mean = 1.15869 PDF variance = 0.202361 Sample size = 1000 Sample mean = 1.16000 Sample variance = 0.244646 Sample maximum = 7 Sample minimum = 1 TEST101 For the Lorentz PDF: LORENTZ_CDF evaluates the CDF; LORENTZ_CDF_INV inverts the CDF. LORENTZ_PDF evaluates the PDF; PDF argument X = 0.750000 PDF value = 0.203718 CDF value = 0.704833 CDF_INV value X = 0.750000 TEST102 For the Lorentz PDF: LORENTZ_MEAN computes the mean; LORENTZ_VARIANCE computes the variance; LORENTZ_SAMPLE samples. PDF mean = 0.00000 PDF variance = 0.340282E+39 Sample size = 1000 Sample mean = -0.986816E-01 Sample variance = 123.129 Sample maximum = 130.165 Sample minimum = -124.778 TEST104 For the Maxwell CDF: MAXWELL_CDF evaluates the CDF. MAXWELL_CDF_INV inverts the CDF. MAXWELL_PDF evaluates the PDF. PDF argument X = 0.500000 PDF parameter A = 2.00000 PDF value 0.241668E-01 CDF value 0.811086E-01 CDF_INV value 0.500000 TEST105 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 = 1.81409 Sample size = 1000 Sample mean = 3.12895 Sample variance = 1.76218 Sample maximum = 8.39485 Sample minimum = 0.257358 TEST106 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 TEST107 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 = 0.125000 0.500000 0.375000 PDF means and variances: 0.625000 0.546875 2.50000 1.25000 1.87500 1.17187 Sample size = 1000 Component Min, Max, Mean, Variance: 1 0 4 0.606000 0.527296 2 0 5 2.50600 1.28325 3 0 5 1.88800 1.17665 TEST108 For the Multinomial PDF: MULTINOMIAL_PDF evaluates the PDF. PDF argument X: 0 2 3 PDF parameter A = 5 PDF parameter B = 3 PDF parameter C = 0.100000 0.500000 0.400000 PDF value = 0.160000 TEST520 For the Nakagami PDF: NAKAGAMI_CDF evaluates the CDF; NAKAGAMI_PDF evaluates the PDF; PDF argument X = 1.25000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF value = 0.393121E-03 CDF value = 0.165738E-04 TEST521 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 TEST109 For the Normal 01 PDF: NORMAL_01_CDF evaluates the CDF; NORMAL_01_CDF_INV inverts the CDF. NORMAL_01_PDF evaluates the PDF; PDF argument X = 1.00000 PDF value = 0.241971 CDF value = 0.841345 CDF_INV value X = 1.00000 TEST110 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 = -0.141043E-02 Sample variance = 0.971822 Sample maximum = 2.91339 Sample minimum = -3.45163 TEST112 For the Normal PDF: NORMAL_CDF evaluates the CDF; NORMAL_CDF_INV inverts the CDF. NORMAL_PDF evaluates the PDF; PDF argument X = 90.0000 PDF parameter A = 100.000 PDF parameter B = 15.0000 PDF value = 0.212965E-01 CDF value = 0.252493 CDF_INV value X = 90.0000 TEST113 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 = 100.659 Sample variance = 242.094 Sample maximum = 146.322 Sample minimum = 56.6507 TEST115 For the Pareto PDF: PARETO_CDF evaluates the CDF; PARETO_CDF_INV inverts the CDF. PARETO_PDF evaluates the PDF; PDF argument X = 4.00000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF value = 0.937500E-01 CDF value = 0.875000 CDF_INV value X = 4.00000 TEST116 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 = 3.05597 Sample variance = 3.58486 Sample maximum = 41.8817 Sample minimum = 2.00007 TEST118 For the Pascal PDF: PASCAL_MEAN computes the mean; PASCAL_SAMPLE samples; PASCAL_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 = 2.63200 Sample variance = 0.775350 Sample maximum = 7 Sample minimum = 2 TEST119 For the Pascal PDF: PASCAL_CDF evaluates the CDF. PASCAL_CDF_INV inverts the CDF. PASCAL_PDF evaluates the PDF. PDF parameter A = 2 PDF parameter B = 0.250000 X PDF(X) CDF(X) CDF_INV(CDF) 0 0.00000 0.00000 2 1 0.00000 0.00000 2 2 0.625000E-01 0.625000E-01 2 3 0.937500E-01 0.156250 3 4 0.105469 0.261719 4 5 0.105469 0.367187 5 6 0.988770E-01 0.466064 6 7 0.889893E-01 0.555054 7 8 0.778656E-01 0.632919 8 9 0.667419E-01 0.699661 9 10 0.563135E-01 0.755975 10 TEST120 For the Pearson 05 PDF: PEARSON_05_PDF evaluates the PDF. PDF argument X = 5.00000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF parameter C = 3.00000 PDF value = 0.758163E-01 TEST121 For the Planck PDF: PLANCK_PDF evaluates the PDF. PDF argument X = 0.500000 PDF value = 0.296718E-01 TEST122 For the Planck PDF: PLANCK_SAMPLE samples. Sample size = 1000 Sample mean = 3.68497 Sample variance = 4.03879 Sample maximum = 11.5466 Sample minimum = 0.290433 TEST1225: POISSON_CDF evaluates the cumulative distribution function for the discrete Poisson probability density function. 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 0.980000 0.980199 0.1000 0 0.905000 0.904837 0.1000 1 0.995000 0.995321 0.5000 0 0.607000 0.606531 0.5000 1 0.910000 0.909796 0.5000 2 0.986000 0.985612 1.0000 0 0.368000 0.367879 1.0000 1 0.736000 0.735759 1.0000 2 0.920000 0.919699 1.0000 3 0.981000 0.981012 2.0000 0 0.135000 0.135335 2.0000 1 0.406000 0.406006 2.0000 2 0.677000 0.676676 2.0000 3 0.857000 0.857123 5.0000 0 0.700000E-02 0.673795E-02 5.0000 1 0.400000E-01 0.404277E-01 5.0000 2 0.125000 0.124652 5.0000 3 0.265000 0.265026 5.0000 4 0.441000 0.440493 5.0000 5 0.616000 0.615961 5.0000 6 0.762000 0.762183 TEST123 For the Poisson PDF: POISSON_CDF evaluates the CDF, POISSON_CDF_INV inverts the CDF. PDF argument X = 7 PDF parameter A = 10.0000 CDF value = 0.220221 CDF_INV value X = 7 TEST124 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 = 9.86500 Sample variance = 9.64639 Sample maximum = 19 Sample minimum = 1 TEST125 For the Poisson PDF: POISSON_PDF evaluates the PDF. POISSON_CDF evaluates the CDF. PDF parameter A = 10.0000 X PDF(X) CDF(X) 0 0.453999E-04 0.453999E-04 1 0.453999E-03 0.499399E-03 2 0.227000E-02 0.276940E-02 3 0.756666E-02 0.103361E-01 4 0.189166E-01 0.292527E-01 5 0.378333E-01 0.670860E-01 6 0.630555E-01 0.130141 7 0.900792E-01 0.220221 8 0.112599 0.332820 9 0.125110 0.457930 10 0.125110 0.583040 TEST126 POLY_VAL evaluates a polynomial. Polynomial degree is N = 3 Polynomial coefficients are: 0 7.00000 1 5.00000 2 2.00000 3 1.00000 Polynomial argument X = 2.00000 Polynomial value VAL = 33.0000 (Expected value is 33.) TEST209 For the Power PDF: POWER_CDF evaluates the CDF; POWER_CDF_INV inverts the CDF. POWER_PDF evaluates the PDF; PDF argument X = 0.600000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF value = 0.133333 CDF value = 0.400000E-01 CDF_INV value X = 0.600000 TEST211 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 = 2.00931 Sample variance = 0.486782 Sample maximum = 2.99995 Sample minimum = 0.643240E-01 TEST127 For the Rayleigh PDF: RAYLEIGH_CDF evaluates the CDF; RAYLEIGH_CDF_INV inverts the CDF. RAYLEIGH_PDF evaluates the PDF; PDF argument X = 1.00000 PDF parameter A = 2.00000 PDF value = 0.220624 CDF value = 0.117503 CDF_INV value X = 1.00000 TEST128 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 = 2.50389 Sample variance = 1.70240 Sample maximum = 8.17104 Sample minimum = 0.586895E-01 TEST380 For the Reciprocal PDF: RECIPROCAL_CDF evaluates the CDF. RECIPROCAL_CDF_INV inverts the CDF. RECIPROCAL_PDF evaluates the PDF. PDF argument X = 1.50000 PDF parameter A = 1.00000 PDF parameter B = 3.00000 PDF value 0.606826 CDF value 0.369070 CDF_INV value X 1.50000 TEST381 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 = 1.82746 Sample variance = 0.330480 Sample maximum = 2.99353 Sample minimum = 1.00090 TEST304 For the Hyperbolic Secant PDF: SECH_CDF evaluates the CDF. SECH_CDF_INV inverts the CDF. SECH_PDF evaluates the PDF. PDF argument X = 4.00000 PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF value 0.141142 CDF value 0.652910 CDF_INV value = 4.00000 TEST305 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 = 9.86961 Sample size = 1000 Sample mean = 3.04869 Sample variance = 9.50086 Sample maximum = 16.0391 Sample minimum = -14.5716 TEST204 For the Semicircular PDF: SEMICIRCULAR_CDF evaluates the CDF. SEMICIRCULAR_CDF_INV inverts the CDF. SEMICIRCULAR_PDF evaluates the PDF. PDF argument X = 4.00000 PDF parameter A = 3.00000 PDF parameter B = 2.00000 PDF value 0.275664 CDF value 0.804499 CDV_INV value X = 4.00000 TEST205 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 = 3.00750 Sample variance = 1.04359 Sample maximum = 4.97761 Sample minimum = 1.01574 TEST129: STUDENT_CENTRAL_CDF evaluates the cumulative distribution function for the Student's central T probability density function. A B C X Exact F STUDENT_CENTRAL_CDF(A,B,C,X) 0.0000 1.0000 1.0000 0.3250 0.600000 0.600023 0.0000 1.0000 2.0000 0.2890 0.600000 0.600108 0.0000 1.0000 3.0000 0.2770 0.600000 0.600115 0.0000 1.0000 4.0000 0.2710 0.600000 0.600099 0.0000 1.0000 5.0000 0.2670 0.600000 0.599934 0.0000 1.0000 2.0000 0.8160 0.750000 0.749886 0.0000 1.0000 5.0000 0.7270 0.750000 0.750088 0.0000 1.0000 2.0000 2.9200 0.950000 0.950000 0.0000 1.0000 5.0000 2.0150 0.950000 0.949997 0.0000 1.0000 2.0000 6.9650 0.990000 0.990001 0.0000 1.0000 3.0000 4.5410 0.990000 0.990002 0.0000 1.0000 4.0000 3.7470 0.990000 0.990000 0.0000 1.0000 5.0000 3.3650 0.990000 0.990001 TEST130 For the central Student PDF: STUDENT_CENTRAL_CDF evaluates the CDF. STUDENT_CENTRAL_PDF evaluates the PDF. PDF argument X = 2.44700 PDF parameter A = 0.500000 PDF parameter B = 2.00000 PDF parameter C = 6.00000 PDF value = 0.147540 CDF value = 0.816049 TEST131 For the central Student PDF: STUDENT_CENTRAL_MEAN computes the mean; STUDENT_CENTRAL_SAMPLE samples; STUDENT_CENTRAL_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 = 0.505245 Sample variance = 4.79491 Sample maximum = 12.1757 Sample minimum = -42.3127 TEST133 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 TEST134 For the Triangular PDF: TRIANGULAR_CDF evaluates the CDF; TRIANGULAR_CDF_INV inverts the CDF. TRIANGULAR_PDF evaluates the PDF; PDF argument X = 4.00000 PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF value = 0.148148 CDF value = 0.222222 CDF_INV value X = 4.00000 TEST135 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 = 5.46170 Sample variance = 3.35096 Sample maximum = 9.80816 Sample minimum = 1.21028 TEST137 For the Uniform 01 Order PDF: UNIFORM_ORDER_SAMPLE samples. Ordered sample: 1 0.334575E-01 2 0.569078E-01 3 0.235631 4 0.303481 5 0.306436 6 0.432032 7 0.629067 8 0.697739 9 0.712700 10 0.823426 TEST138 For the Uniform PDF on the N-Sphere: UNIFORM_NSPHERE_SAMPLE samples. Dimension N of sphere = 3 Points on the sphere: 1 0.668052 0.812311E-01 -0.739668 2 -0.255642 -0.938918 0.230391 3 0.485317 0.547918E-01 0.872620 4 -0.376687 -0.863005 -0.336646 5 0.974597 -0.203726 0.930388E-01 6 0.405481 0.818128 -0.407739 7 0.781901 -0.510972 0.357124 8 0.557327 -0.653946 -0.511606 9 0.466223 -0.191594 0.863671 10 0.515624 -0.464859 0.719749 TEST139 For the Uniform PDF: UNIFORM_CDF evaluates the CDF; UNIFORM_CDF_INV inverts the CDF. UNIFORM_PDF evaluates the PDF; PDF argument X = 4.00000 PDF parameter A = 1.00000 PDF parameter B = 10.0000 PDF value = 0.111111 CDF value = 0.333333 CDF_INV value X = 4.00000 TEST140 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 = 5.35820 Sample variance = 6.68640 Sample maximum = 9.98782 Sample minimum = 1.00149 TEST142 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 argument X = 4 PDF parameter A = 1 PDF parameter B = 6 PDF value = 0.166667 CDF value = 0.666667 CDF_INV value X2 = 5 TEST143 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 = 3.93400 Sample variance = 2.70434 Sample maximum = 6 Sample minimum = 1 TEST144 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 TEST145 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 argument X = 0.500000 PDF parameter A = 1.00000 PDF parameter B = 2.00000 PDF value = 0.403853 CDF value = 0.261808 CDF_INV value X = 0.499922 TEST146 For the Von Mises PDF: VON_MISES_MEAN computes the mean; VON_MISES_SAMPLE samples. PDF parameter A = 1.00000 PDF parameter B = 2.00000 Sample size = 1000 Sample mean = 1.03534 Sample variance = 0.796658 Sample maximum = 3.94483 Sample minimum = -2.13944 TEST148 For the Weibull PDF: WEIBULL_CDF evaluates the CDF; WEIBULL_CDF_INV inverts the CDF. WEIBULL_PDF evaluates the PDF; PDF argument X = 3.00000 PDF parameter A = 2.00000 PDF parameter B = 3.00000 PDF parameter C = 4.00000 PDF value = 0.487768E-01 CDF value = 0.122698E-01 CDF_INV value X = 3.00000 TEST149 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 = 0.581954 Sample size = 1000 Sample mean = 4.67663 Sample variance = 0.576884 Sample maximum = 7.27132 Sample minimum = 2.19019 TEST151 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 argument X = 2 PDF parameter A = 0.500000 PDF parameter B = 1.50000 PDF value = 0.113508 CDF value = 0.972723 CDF_INV value X = 3 TEST152 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 TEST153 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 = 0.635660 Sample maximum = 4 Sample minimum = 0 TEST154 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 TEST155 For the Zipf PDF: ZIPF_SAMPLE samples. PDF parameter A = 4.00000 PDF mean = 1.11063 PDF variance = 0.286327 Sample size = 1000 Sample mean = 1.10400 Sample variance = 0.191376 Sample maximum = 8 Sample minimum = 1 PROB_PRB Normal end of execution.