PROB - Probability Density Functions

PROB contains routines for handling various discrete and continuous probability density functions or "PDF"'s. For a discrete variable, PDF(X) is the probability that the value X will occur; for a continuous variable PDF(X) is the probability density of X.

The corresponding cumulative density functions or "CDF"'s are also handled. For a discrete or continuous variable, CDF(X) is the probability that the variable takes on a value less than or equal to X.

For most distributions, the mean or "average value" or "expected value" is also available. For a discrete variable, MEAN is simply the sum of the products X * PDF(X); for a continuous variable, MEAN is the integral of X * PDF(X) over the range. For the distributions covered here, the means are known beforehand, and no summation or integration is required.

For most distributions, the variance is available. For a discrete variable, the variance is the sum of the products ( X - MEAN )**2 * PDF(X); for a continuous variable, the variance is the integral of ( X - MEAN )**2 * PDF(X) over the range. The square root of the variance is known as the standard deviation. For the distributions covered here, the variances are known beforehand, and no summation or integration is required.

Reference 1:

Evans, Hastings and Peacock,
Statistical Distributions

Reference 2:

Johnson, Kotz, and Balakrishnan,
Continuous Univariate Distributions, second edition,
Wiley, 1994.

Reference 3:

Michael McLaughlin
A Compendium of Common Probability Distributions

Reference 4:

Zwillinger and Kokoska
Standard Probability and Statistical Tables
CRC Press, 2000, ISBN 1-58488-059-7.

Files you may copy include:

• prob.f90, the source code;
• prob_prb.f90, the calling program;
• prob_prb.out, the sample output.

The list of routines includes:

• ANGLIT_CDF evaluates the Anglit CDF.
• ANGLIT_CDF_INV inverts the Anglit CDF.
• ANGLIT_MEAN returns the mean of the Anglit PDF.
• ANGLIT_PDF evaluates the Anglit PDF.
• ANGLIT_SAMPLE samples the Anglit PDF.
• ANGLIT_VARIANCE returns the variance of the Anglit PDF.
• ARCSIN_CDF evaluates the Arcsin CDF.
• ARCSIN_CDF_INV inverts the Arcsin CDF.
• ARCSIN_MEAN returns the mean of the Arcsin PDF.
• ARCSIN_PDF evaluates the Arcsin PDF.
• ARCSIN_SAMPLE samples the Arcsin PDF.
• ARCSIN_VARIANCE returns the variance of the Arcsin PDF.
• BENFORD_PDF returns the Benford probability of one or more significant digits.
• BERNOULLI_CDF evaluates the Bernoulli CDF.
• BERNOULLI_CDF_INV inverts the Bernoulli CDF.
• BERNOULLI_CHECK checks the parameter of the Bernoulli CDF.
• BERNOULLI_MEAN returns the mean of the Bernoulli PDF.
• BERNOULLI_PDF evaluates the Bernoulli PDF.
• BERNOULLI_SAMPLE samples the Bernoulli PDF.
• BERNOULLI_VARIANCE returns the variance of the Bernoulli PDF.
• BETA returns the value of the Beta function.
• BETA_BINOMIAL_CDF evaluates the Beta Binomial CDF.
• BETA_BINOMIAL_CDF_INV inverts the Beta Binomial CDF.
• BETA_BINOMIAL_CHECK checks the parameters of the Beta Binomial PDF.
• BETA_BINOMIAL_MEAN returns the mean of the Beta Binomial PDF.
• BETA_BINOMIAL_PDF evaluates the Beta Binomial PDF.
• BETA_BINOMIAL_SAMPLE samples the Beta Binomial CDF.
• BETA_BINOMIAL_VARIANCE returns the variance of the Beta Binomial PDF.
• BETA_CDF evaluates the Beta CDF.
• BETA_CDF_INV inverts the Beta CDF.
• BETA_CHECK checks the parameters of the Beta PDF.
• BETA_INC returns the value of the incomplete Beta function.
• BETA_INC_VALUES returns some values of the incomplete Beta function.
• BETA_MEAN returns the mean of the Beta PDF.
• BETA_PASCAL_CDF evaluates the Beta Pascal CDF.
• BETA_PASCAL_CDF_INV inverts the Beta Pascal CDF.
• BETA_PASCAL_CHECK checks the parameters of the Beta Pascal PDF.
• BETA_PASCAL_MEAN returns the mean of the Beta Pascal PDF.
• BETA_PASCAL_PDF evaluates the Beta Pascal PDF.
• BETA_PASCAL_SAMPLE samples the Beta Pascal CDF.
• BETA_PASCAL_VARIANCE returns the variance of the Beta Pascal PDF.
• BETA_PDF evaluates the Beta PDF.
• BETA_SAMPLE samples the Beta PDF.
• BETA_VARIANCE returns the variance of the Beta PDF.
• BINOMIAL_CDF evaluates the Binomial CDF.
• BINOMIAL_CDF_VALUES returns some values of the binomial CDF.
• BINOMIAL_CDF_INV inverts the Binomial CDF.
• BINOMIAL_CHECK checks the parameter of the Binomial PDF.
• BINOMIAL_COEF computes the Binomial coefficient C(N,K).
• BINOMIAL_COEF_LOG computes the logarithm of the Binomial coefficient.
• BINOMIAL_MEAN returns the mean of the Binomial PDF.
• BINOMIAL_PDF evaluates the Binomial PDF.
• BINOMIAL_SAMPLE samples the Binomial PDF.
• BINOMIAL_VARIANCE returns the variance of the Binomial PDF.
• BRADFORD_CDF evaluates the Bradford CDF.
• BRADFORD_CDF_INV inverts the Bradford CDF.
• BRADFORD_CHECK checks the parameters of the Bradford PDF.
• BRADFORD_MEAN returns the mean of the Bradford PDF.
• BRADFORD_PDF evaluates the Bradford PDF.
• BRADFORD_SAMPLE samples the Bradford PDF.
• BRADFORD_VARIANCE returns the variance of the Bradford PDF.
• BURR_CDF evaluates the Burr CDF.
• BURR_CDF_INV inverts the Burr CDF.
• BURR_CHECK checks the parameters of the Burr CDF.
• BURR_MEAN returns the mean of the Burr PDF.
• BURR_PDF evaluates the Burr PDF.
• BURR_SAMPLE samples the Burr PDF.
• BURR_VARIANCE returns the variance of the Burr PDF.
• CAUCHY_CDF evaluates the Cauchy CDF.
• CAUCHY_CDF_INV inverts the Cauchy CDF.
• CAUCHY_CHECK checks the parameters of the Cauchy CDF.
• CAUCHY_MEAN returns the mean of the Cauchy PDF.
• CAUCHY_PDF evaluates the Cauchy PDF.
• CAUCHY_SAMPLE samples the Cauchy PDF.
• CAUCHY_VARIANCE returns the variance of the Cauchy PDF.
• CHI_CDF evaluates the Chi CDF.
• CHI_CDF_INV inverts the Chi CDF.
• CHI_CHECK checks the parameters of the Chi CDF.
• CHI_MEAN returns the mean of the Chi PDF.
• CHI_PDF evaluates the Chi PDF.
• CHI_SAMPLE samples the Chi PDF.
• CHI_VARIANCE returns the variance of the Chi PDF.
• CHISQUARE_CENTRAL_CDF evaluates the chi-squared CDF.
• CHISQUARE_CENTRAL_CDF_INV inverts the chi-squared PDF.
• CHISQUARE_CENTRAL_CDF_VALUES returns values of the Chi-Square central CDF.
• CHISQUARE_CENTRAL_CHECK checks the parameter of the central Chi-Squared PDF.
• CHISQUARE_CENTRAL_MEAN returns the mean of the central Chi-Squared PDF.
• CHISQUARE_CENTRAL_PDF evaluates the central Chi-Squared PDF.
• CHISQUARE_CENTRAL_SAMPLE samples the central Chisquare PDF.
• CHISQUARE_CENTRAL_VARIANCE returns the variance of the central Chisquare PDF.
• CHISQUARE_NONCENTRAL_CHECK checks the parameters of the noncentral Chi-Squared PDF.
• CHISQUARE_NONCENTRAL_MEAN returns the mean of the noncentral Chi-Squared PDF.
• CHISQUARE_NONCENTRAL_SAMPLE samples the noncentral Chisquare PDF.
• CHISQUARE_NONCENTRAL_VARIANCE returns the variance of the noncentral Chi-Squared PDF.
• CIRCLE_SAMPLE samples points from a circle.
• CIRCULAR_NORMAL_01_MEAN returns the mean of the Circular Normal 01 PDF.
• CIRCULAR_NORMAL_01_PDF evaluates the Circular Normal 01 PDF.
• CIRCULAR_NORMAL_01_SAMPLE samples the Circular Normal 01 PDF.
• CIRCULAR_NORMAL_01_VARIANCE returns the variance of the Circular Normal 01 PDF.
• COSINE_CDF evaluates the Cosine CDF.
• COSINE_CDF_INV inverts the Cosine CDF.
• COSINE_CHECK checks the parameters of the Cosine CDF.
• COSINE_MEAN returns the mean of the Cosine PDF.
• COSINE_PDF evaluates the Cosine PDF.
• COSINE_SAMPLE samples the Cosine PDF.
• COSINE_VARIANCE returns the variance of the Cosine PDF.
• COUPON_MEAN returns the variance of the Coupon PDF.
• COUPON_SIMULATE simulates the coupon collector's problem.
• COUPON_VARIANCE returns the variance of the Coupon PDF.
• CSC returns the cosecant of X.
• DERANGED_CDF evaluates the Deranged CDF.
• DERANGED_CDF_INV inverts the Deranged CDF.
• DERANGED_CHECK checks the parameter of the Deranged PDF.
• DERANGED_ENUM returns the number of derangements of N objects.
• DERANGED_MEAN returns the mean of the Deranged CDF.
• DERANGED_PDF evaluates the Deranged PDF.
• DERANGED_SAMPLE samples the Deranged PDF.
• DERANGED_VARIANCE returns the variance of the Deranged CDF.
• DIGAMMA calculates the digamma or Psi function = d ( LOG ( GAMMA ( X ) ) ) / dX
• DIPOLE_CDF evaluates the Dipole CDF.
• DIPOLE_CDF_INV inverts the Dipole CDF.
• DIPOLE_CHECK checks the parameters of the Dipole CDF.
• DIPOLE_PDF evaluates the Dipole PDF.
• DIPOLE_SAMPLE samples the Dipole PDF.
• DIRICHLET_CHECK checks the parameters of the Dirichlet PDF.
• DIRICHLET_MEAN returns the means of the Dirichlet PDF.
• DIRICHLET_MIX_CHECK checks the parameters of a Dirichlet mixture PDF.
• DIRICHLET_MIX_MEAN returns the means of a Dirichlet mixture PDF.
• DIRICHLET_MIX_PDF evaluates a Dirichlet mixture PDF.
• DIRICHLET_MIX_SAMPLE samples a Dirichlet mixture PDF.
• DIRICHLET_MOMENT2 returns the second moments of the Dirichlet PDF.
• DIRICHLET_MULTINOMIAL_PDF evaluates a Dirichlet Multinomial PDF.
• DIRICHLET_PDF evaluates the Dirichlet PDF.
• DIRICHLET_SAMPLE samples the Dirichlet PDF.
• DIRICHLET_VARIANCE returns the variances of the Dirichlet PDF.
• DISCRETE_CDF evaluates the Discrete CDF.
• DISCRETE_CDF_INV inverts the Discrete CDF.
• DISCRETE_CHECK checks the parameters of the Discrete CDF.
• DISCRETE_MEAN evaluates the mean of the Discrete PDF.
• DISCRETE_PDF evaluates the Discrete PDF.
• DISCRETE_SAMPLE samples the Discrete PDF.
• DISCRETE_VARIANCE evaluates the variance of the Discrete PDF.
• E_CONSTANT returns the value of E.
• EMPIRICAL_DISCRETE_CDF evaluates the Empirical Discrete CDF.
• EMPIRICAL_DISCRETE_CDF_INV inverts the Empirical Discrete CDF.
• EMPIRICAL_DISCRETE_CHECK checks the parameters of the Empirical Discrete CDF.
• EMPIRICAL_DISCRETE_MEAN returns the mean of the Empirical Discrete PDF.
• EMPIRICAL_DISCRETE_PDF evaluates the Empirical Discrete PDF.
• EMPIRICAL_DISCRETE_SAMPLE samples the Empirical Discrete PDF.
• EMPIRICAL_DISCRETE_VARIANCE returns the variance of the Empirical Discrete PDF.
• ERLANG_CDF evaluates the Erlang CDF.
• ERLANG_CDF_INV inverts the Erlang CDF.
• ERLANG_CHECK checks the parameters of the Erlang PDF.
• ERLANG_MEAN returns the mean of the Erlang PDF.
• ERLANG_PDF evaluates the Erlang PDF.
• ERLANG_SAMPLE samples the Erlang PDF.
• ERLANG_VARIANCE returns the variance of the Erlang PDF.
• ERROR_FUNCTION evaluates the error function ERF(X).
• EULER_CONSTANT returns the value of the Euler-Mascheroni constant.
• EXPONENTIAL_01_CDF evaluates the Exponential 01 CDF.
• EXPONENTIAL_01_CDF_INV inverts the Exponential 01 CDF.
• EXPONENTIAL_01_MEAN returns the mean of the Exponential 01 PDF.
• EXPONENTIAL_01_PDF evaluates the Exponential 01 PDF.
• EXPONENTIAL_01_SAMPLE samples the Exponential PDF with parameter 1.
• EXPONENTIAL_01_VARIANCE returns the variance of the Exponential 01 PDF.
• EXPONENTIAL_CDF evaluates the Exponential CDF.
• EXPONENTIAL_CDF_INV inverts the Exponential CDF.
• EXPONENTIAL_CHECK checks the parameters of the Exponential CDF.
• EXPONENTIAL_MEAN returns the mean of the Exponential PDF.
• EXPONENTIAL_PDF evaluates the Exponential PDF.
• EXPONENTIAL_SAMPLE samples the Exponential PDF.
• EXPONENTIAL_VARIANCE returns the variance of the Exponential PDF.
• EXTREME_CDF evaluates the Extreme Value CDF.
• EXTREME_CDF_INV inverts the Extreme Value CDF.
• EXTREME_CHECK checks the parameters of the Extreme Value CDF.
• EXTREME_MEAN returns the mean of the Extreme Value PDF.
• EXTREME_PDF evaluates the Extreme Value PDF.
• EXTREME_SAMPLE samples the Extreme Value PDF.
• EXTREME_VARIANCE returns the variance of the Extreme Value PDF.
• F_CENTRAL_CDF evaluates the F central CDF.
• F_CENTRAL_CDF_VALUES returns some values of the F central CDF test function.
• F_CENTRAL_MEAN returns the mean of the F central PDF.
• F_CENTRAL_PDF evaluates the F central PDF.
• F_CENTRAL_SAMPLE samples the F central PDF.
• F_CENTRAL_VARIANCE returns the variance of the F central PDF.
• F_NONCENTRAL_MEAN returns the mean of the F noncentral PDF.
• F_NONCENTRAL_VARIANCE returns the variance of the F noncentral PDF.
• FACTORIAL_LOG returns the logarithm of N!.
• FACTORIAL_STIRLING computes Stirling's approximation to N!.
• FISK_CDF evaluates the Fisk CDF.
• FISK_CDF_INV inverts the Fisk CDF.
• FISK_CHECK checks the parameters of the Fisk PDF.
• FISK_MEAN returns the mean of the Fisk PDF.
• FISK_PDF evaluates the Fisk PDF.
• FISK_SAMPLE samples the Fisk PDF.
• FISK_VARIANCE returns the variance of the Fisk PDF.
• FOLDED_NORMAL_CDF evaluates the Folded Normal CDF.
• FOLDED_NORMAL_CDF_INV inverts the Folded Normal CDF.
• FOLDED_NORMAL_CHECK checks the parameters of the Folded Normal CDF.
• FOLDED_NORMAL_MEAN returns the mean of the Folded Normal PDF.
• FOLDED_NORMAL_PDF evaluates the Folded Normal PDF.
• FOLDED_NORMAL_SAMPLE samples the Folded Normal PDF.
• FOLDED_NORMAL_VARIANCE returns the variance of the Folded Normal PDF.
• GAMMA calculates the Gamma function for a real argument X.
• GAMMA_CDF evaluates the Gamma CDF.
• GAMMA_CHECK checks the parameters of the Gamma PDF.
• GAMMA_INC computes the incomplete Gamma function.
• GAMMA_INC_VALUES returns some values of the incomplete Gamma function.
• GAMMA_LOG calculates the natural logarithm of GAMMA ( X ) for positive X.
• GAMMA_LOG_INT computes the logarithm of Gamma of an integer N.
• GAMMA_MEAN returns the mean of the Gamma PDF.
• GAMMA_PDF evaluates the Gamma PDF.
• GAMMA_SAMPLE samples the Gamma PDF.
• GAMMA_VARIANCE returns the variance of the Gamma PDF.
• GENLOGISTIC_CDF evaluates the Generalized Logistic CDF.
• GENLOGISTIC_CDF_INV inverts the Generalized Logistic CDF.
• GENLOGISTIC_CHECK checks the parameters of the Generalized Logistic CDF.
• GENLOGISTIC_MEAN returns the mean of the Generalized Logistic PDF.
• GENLOGISTIC_PDF evaluates the Generalized Logistic PDF.
• GENLOGISTIC_SAMPLE samples the Generalized Logistic PDF.
• GENLOGISTIC_VARIANCE returns the variance of the Generalized Logistic PDF.
• GEOMETRIC_CDF evaluates the Geometric CDF.
• GEOMETRIC_CDF_INV inverts the Geometric CDF.
• GEOMETRIC_CHECK checks the parameter of the Geometric CDF.
• GEOMETRIC_MEAN returns the mean of the Geometric PDF.
• GEOMETRIC_PDF evaluates the Geometric PDF.
• GEOMETRIC_SAMPLE samples the Geometric PDF.
• GEOMETRIC_VARIANCE returns the variance of the Geometric PDF.
• GOMPERTZ_CDF evaluates the Gompertz CDF.
• GOMPERTZ_CDF_INV inverts the Gompertz CDF.
• GOMPERTZ_CHECK checks the parameters of the Gompertz PDF.
• GOMPERTZ_PDF evaluates the Gompertz PDF.
• GOMPERTZ_SAMPLE samples the Gompertz PDF.
• GUMBEL_CDF evaluates the Gumbel CDF.
• GUMBEL_CDF_INV inverts the Gumbel CDF.
• GUMBEL_MEAN returns the mean of the Gumbel PDF.
• GUMBEL_PDF evaluates the Gumbel PDF.
• GUMBEL_SAMPLE samples the Gumbel PDF.
• GUMBEL_VARIANCE returns the variance of the Gumbel PDF.
• HALF_NORMAL_CDF evaluates the Half Normal CDF.
• HALF_NORMAL_CDF_INV inverts the Half Normal CDF.
• HALF_NORMAL_CHECK checks the parameters of the Half Normal PDF.
• HALF_NORMAL_MEAN returns the mean of the Half Normal PDF.
• HALF_NORMAL_PDF evaluates the Half Normal PDF.
• HALF_NORMAL_SAMPLE samples the Half Normal PDF.
• HALF_NORMAL_VARIANCE returns the variance of the Half Normal PDF.
• HYPERGEOMETRIC_CDF evaluates the Hypergeometric CDF.
• HYPERGEOMETRIC_CHECK checks the parameters of the Hypergeometric CDF.
• HYPERGEOMETRIC_MEAN returns the mean of the Hypergeometric PDF.
• HYPERGEOMETRIC_PDF evaluates the Hypergeometric PDF.
• HYPERGEOMETRIC_SAMPLE samples the Hypergeometric PDF.
• HYPERGEOMETRIC_VARIANCE returns the variance of the Hypergeometric PDF.
• I_FACTORIAL returns N!.
• I_RANDOM returns a random integer in a given range.
• I_ROUNDUP rounds a real value "up" to the nearest integer.
• I0 evaluates the modified Bessel function of the first kind and order zero.
• INVERSE_GAUSSIAN_CDF evaluates the Inverse Gaussian CDF.
• INVERSE_GAUSSIAN_CHECK checks the parameters of the Inverse Gaussian CDF.
• INVERSE_GAUSSIAN_MEAN returns the mean of the Inverse Gaussian PDF.
• INVERSE_GAUSSIAN_PDF evaluates the Inverse Gaussian PDF.
• INVERSE_GAUSSIAN_SAMPLE samples the Inverse Gaussian PDF.
• INVERSE_GAUSSIAN_VARIANCE returns the variance of the Inverse Gaussian PDF.
• IROW_MAX returns the maximums of rows of an integer array.
• IROW_MEAN returns the means of the rows of a table.
• IROW_MIN returns the minimums of rows of an integer array.
• IROW_VARIANCE returns the variances of the rows of a table.
• IVEC_MAX computes the maximum element of an integer array.
• IVEC_MEAN returns the mean of an integer vector.
• IVEC_MIN computes the minimum element of an integer array.
• IVEC_PRINT prints an integer vector.
• IVEC_VARIANCE returns the variance of an integer vector.
• LAPLACE_CDF evaluates the Laplace CDF.
• LAPLACE_CDF_INV inverts the Laplace CDF.
• LAPLACE_CHECK checks the parameters of the Laplace PDF.
• LAPLACE_MEAN returns the mean of the Laplace PDF.
• LAPLACE_PDF evaluates the Laplace PDF.
• LAPLACE_SAMPLE samples the Laplace PDF.
• LAPLACE_VARIANCE returns the variance of the Laplace PDF.
• LERCH estimates the Lerch transcendent function.
• LOGISTIC_CDF evaluates the Logistic CDF.
• LOGISTIC_CDF_INV inverts the Logistic CDF.
• LOGISTIC_CHECK checks the parameters of the Logistic CDF.
• LOGISTIC_MEAN returns the mean of the Logistic PDF.
• LOGISTIC_PDF evaluates the Logistic PDF.
• LOGISTIC_SAMPLE samples the Logistic PDF.
• LOGISTIC_VARIANCE returns the variance of the Logistic PDF.
• LOGNORMAL_CDF evaluates the Lognormal CDF.
• LOGNORMAL_CDF_INV inverts the Lognormal CDF.
• LOGNORMAL_CHECK checks the parameters of the Lognormal PDF.
• LOGNORMAL_MEAN returns the mean of the Lognormal PDF.
• LOGNORMAL_PDF evaluates the Lognormal PDF.
• LOGNORMAL_SAMPLE samples the Lognormal PDF.
• LOGNORMAL_VARIANCE returns the variance of the Lognormal PDF.
• LOGSERIES_CDF evaluates the Logarithmic Series CDF.
• LOGSERIES_CDF_INV inverts the Logarithmic Series CDF.
• LOGSERIES_CHECK checks the parameter of the Logarithmic Series PDF.
• LOGSERIES_MEAN returns the mean of the Logarithmic Series PDF.
• LOGSERIES_PDF evaluates the Logarithmic Series PDF.
• LOGSERIES_SAMPLE samples the Logarithmic Series PDF.
• LOGSERIES_VARIANCE returns the variance of the Logarithmic Series PDF.
• LORENTZ_CDF evaluates the Lorentz CDF.
• LORENTZ_CDF_INV inverts the Lorentz CDF.
• LORENTZ_MEAN returns the mean of the Lorentz PDF.
• LORENTZ_PDF evaluates the Lorentz PDF.
• LORENTZ_SAMPLE samples the Lorentz PDF.
• LORENTZ_VARIANCE returns the variance of the Lorentz PDF.
• MAXWELL_CDF evaluates the Maxwell CDF.
• MAXWELL_CDF_INV inverts the Maxwell CDF.
• MAXWELL_CHECK checks the parameters of the Maxwell CDF.
• MAXWELL_MEAN returns the mean of the Maxwell PDF.
• MAXWELL_PDF evaluates the Maxwell PDF.
• MAXWELL_SAMPLE samples the Maxwell PDF.
• MAXWELL_VARIANCE returns the variance of the Maxwell PDF.
• MULTICOEF_CHECK checks the parameters of the multinomial coefficient.
• MULTINOMIAL_COEF1 computes a Multinomial coefficient.
• MULTINOMIAL_COEF2 computes a Multinomial coefficient.
• MULTINOMIAL_CHECK checks the parameters of the Multinomial PDF.
• MULTINOMIAL_COVARIANCE returns the covariances of the Multinomial PDF.
• MULTINOMIAL_MEAN returns the means of the Multinomial PDF.
• MULTINOMIAL_PDF computes a Multinomial PDF.
• MULTINOMIAL_SAMPLE samples the Multinomial PDF.
• MULTINOMIAL_VARIANCE returns the variances of the Multinomial PDF.
• MULTIVARIATE_NORMAL_SAMPLE samples the Multivariate Normal PDF.
• NAKAGAMI_CDF evaluates the Nakagami CDF.
• NAKAGAMI_CHECK checks the parameters of the Nakagami PDF.
• NAKAGAMI_MEAN returns the mean of the Nakagami PDF.
• NAKAGAMI_PDF evaluates the Nakagami PDF.
• NAKAGAMI_VARIANCE returns the variance of the Nakagami PDF.
• NORMAL_01_CDF evaluates the Normal 01 CDF.
• NORMAL_01_CDF_INV inverts the Normal 01 CDF.
• NORMAL_01_MEAN returns the mean of the Normal 01 PDF.
• NORMAL_01_PDF evaluates the Normal 01 PDF.
• NORMAL_01_SAMPLE samples the standard Normal PDF.
• NORMAL_01_VARIANCE returns the variance of the Normal 01 PDF.
• NORMAL_CDF evaluates the Normal CDF.
• NORMAL_CDF_INV inverts the Normal CDF.
• NORMAL_CHECK checks the parameters of the Normal PDF.
• NORMAL_MEAN returns the mean of the Normal PDF.
• NORMAL_PDF evaluates the Normal PDF.
• NORMAL_SAMPLE samples the Normal PDF.
• NORMAL_VARIANCE returns the variance of the Normal PDF.
• PARETO_CDF evaluates the Pareto CDF.
• PARETO_CDF_INV inverts the Pareto CDF.
• PARETO_CHECK checks the parameters of the Pareto CDF.
• PARETO_MEAN returns the mean of the Pareto PDF.
• PARETO_PDF evaluates the Pareto PDF.
• PARETO_SAMPLE samples the Pareto PDF.
• PARETO_VARIANCE returns the variance of the Pareto PDF.
• PASCAL_CDF evaluates the Pascal CDF.
• PASCAL_CDF_INV inverts the Pascal CDF.
• PASCAL_CHECK checks the parameters of the Pascal PDF.
• PASCAL_MEAN returns the mean of the Pascal PDF.
• PASCAL_PDF evaluates the Pascal PDF.
• PASCAL_SAMPLE samples the Pascal PDF.
• PASCAL_VARIANCE returns the variance of the Pascal PDF.
• PEARSON_05_CHECK checks the parameters of the Pearson 5 PDF.
• PEARSON_05_MEAN evaluates the mean of the Pearson 5 PDF.
• PEARSON_05_PDF evaluates the Pearson 5 PDF.
• PEARSON_05_SAMPLE samples the Pearson 5 PDF.
• PI returns the value of Pi.
• PLANCK_MEAN returns the mean of the Planck PDF.
• PLANCK_PDF evaluates the Planck PDF.
• PLANCK_SAMPLE samples the Planck PDF.
• PLANCK_VARIANCE returns the variance of the Planck PDF.
• POISSON_CDF evaluates the Poisson CDF.
• POISSON_CDF_VALUES returns some values of the Poisson CDF.
• POISSON_CDF_INV inverts the Poisson CDF.
• POISSON_CHECK checks the parameter of the Poisson PDF.
• POISSON_MEAN returns the mean of the Poisson PDF.
• POISSON_PDF evaluates the Poisson PDF.
• POISSON_SAMPLE samples the Poisson PDF.
• POISSON_VARIANCE returns the variance of the Poisson PDF.
• POLY_VAL evaluates a polynomial using Horner's method.
• POWER_CDF evaluates the Power CDF.
• POWER_CDF_INV inverts the Power CDF.
• POWER_CHECK checks the parameter of the Power PDF.
• POWER_MEAN returns the mean of the Power PDF.
• POWER_PDF evaluates the Power PDF.
• POWER_SAMPLE samples the Power PDF.
• POWER_VARIANCE returns the variance of the Power PDF.
• R_FACTORIAL returns N!.
• R_RANDOM returns a random real in a given range.
• RAYLEIGH_CDF evaluates the Rayleigh CDF.
• RAYLEIGH_CDF_INV inverts the Rayleigh CDF.
• RAYLEIGH_CHECK checks the parameter of the Rayleigh PDF.
• RAYLEIGH_MEAN returns the mean of the Rayleigh PDF.
• RAYLEIGH_PDF evaluates the Rayleigh PDF.
• RAYLEIGH_SAMPLE samples the Rayleigh PDF.
• RAYLEIGH_VARIANCE returns the variance of the Rayleigh PDF.
• RECIPROCAL_CDF evaluates the Reciprocal CDF.
• RECIPROCAL_CDF_INV inverts the Reciprocal CDF.
• RECIPROCAL_CHECK checks the parameters of the Reciprocal CDF.
• RECIPROCAL_MEAN returns the mean of the Reciprocal PDF.
• RECIPROCAL_PDF evaluates the Reciprocal PDF.
• RECIPROCAL_SAMPLE samples the Reciprocal PDF.
• RECIPROCAL_VARIANCE returns the variance of the Reciprocal PDF.
• RROW_MAX returns the maximums of rows of a real array.
• RROW_MEAN returns the means of rows of a real array.
• RROW_MIN returns the minimums of rows of a real array.
• RROW_VARIANCE returns the variances of the rows of a real array.
• RVEC_MAX returns the maximum value in a real vector.
• RVEC_MEAN returns the mean of a real vector.
• RVEC_MIN returns the minimum value of a real array.
• RVEC_PRINT prints a real vector.
• RVEC_UNIT_SUM normalizes a real vector to have unit sum.
• RVEC_VARIANCE returns the variance of a real vector.
• SECH returns the hyperbolic secant.
• SECH_CDF evaluates the Hyperbolic Secant CDF.
• SECH_CDF_INV inverts the Hyperbolic Secant CDF.
• SECH_CHECK checks the parameters of the Hyperbolic Secant CDF.
• SECH_MEAN returns the mean of the Hyperbolic Secant PDF.
• SECH_PDF evaluates the Hypebolic Secant PDF.
• SECH_SAMPLE samples the Hyperbolic Secant PDF.
• SECH_VARIANCE returns the variance of the Hyperbolic Secant PDF.
• SEMICIRCULAR_CDF evaluates the Semicircular CDF.
• SEMICIRCULAR_CDF_INV inverts the Semicircular CDF.
• SEMICIRCULAR_CHECK checks the parameters of the Semicircular CDF.
• SEMICIRCULAR_MEAN returns the mean of the Semicircular PDF.
• SEMICIRCULAR_PDF evaluates the Semicircular PDF.
• SEMICIRCULAR_SAMPLE samples the Semicircular PDF.
• SEMICIRCULAR_VARIANCE returns the variance of the Semicircular PDF.
• STUDENT_CENTRAL_CDF evaluates the central Student T CDF.
• STUDENT_CENTRAL_CDF_VALUES returns some values of the Student Central CDF.
• STUDENT_CENTRAL_CHECK checks the parameter of the central Student T CDF.
• STUDENT_CENTRAL_MEAN returns the mean of the central Student T PDF.
• STUDENT_CENTRAL_PDF evaluates the central Student T PDF.
• STUDENT_CENTRAL_SAMPLE samples the central Student T PDF.
• STUDENT_CENTRAL_VARIANCE returns the variance of the central Student T PDF.
• STUDENT_NONCENTRAL_CDF evaluates the noncentral Student T CDF.
• TFN calculates the T function of Owen.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TRIANGULAR_CDF evaluates the Triangular CDF.
• TRIANGULAR_CDF_INV inverts the Triangular CDF.
• TRIANGULAR_CHECK checks the parameters of the Triangular CDF.
• TRIANGULAR_MEAN returns the mean of the Triangular PDF.
• TRIANGULAR_PDF evaluates the Triangular PDF.
• TRIANGULAR_SAMPLE samples the Triangular PDF.
• TRIANGULAR_VARIANCE returns the variance of the Triangular PDF.
• TRIGAMMA calculates trigamma(x) = d**2 log(Gamma(x)) / dx**2.
• UNIFORM_01_CDF evaluates the Uniform 01 CDF.
• UNIFORM_01_CDF_INV inverts the Uniform 01 CDF.
• UNIFORM_01_MEAN returns the mean of the Uniform 01 PDF.
• UNIFORM_01_ORDER_SAMPLE samples the Uniform 01 Order PDF.
• UNIFORM_01_PDF evaluates the Uniform 01 PDF.
• UNIFORM_01_SAMPLE is a portable random number generator.
• UNIFORM_01_VARIANCE returns the variance of the Uniform 01 PDF.
• UNIFORM_CDF evaluates the Uniform CDF.
• UNIFORM_CDF_INV inverts the Uniform CDF.
• UNIFORM_CHECK checks the parameters of the Uniform CDF.
• UNIFORM_MEAN returns the mean of the Uniform PDF.
• UNIFORM_PDF evaluates the Uniform PDF.
• UNIFORM_SAMPLE samples the Uniform PDF.
• UNIFORM_VARIANCE returns the variance of the Uniform PDF.
• UNIFORM_DISCRETE_CDF evaluates the Uniform Discrete CDF.
• UNIFORM_DISCRETE_CDF_INV inverts the Uniform Discrete CDF.
• UNIFORM_DISCRETE_CHECK checks the parameters of the Uniform discrete CDF.
• UNIFORM_DISCRETE_MEAN returns the mean of the Uniform discrete PDF.
• UNIFORM_DISCRETE_PDF evaluates the Uniform discrete PDF.
• UNIFORM_DISCRETE_SAMPLE samples the Uniform discrete PDF.
• UNIFORM_DISCRETE_VARIANCE returns the variance of the Uniform discrete PDF.
• UNIFORM_NSPHERE_SAMPLE samples the Uniform Unit Sphere PDF.
• VON_MISES_CDF evaluates the Von Mises CDF.
• VON_MISES_CDF_INV inverts the Von Mises CDF.
• VON_MISES_CHECK checks the parameters of the Von Mises PDF.
• VON_MISES_MEAN returns the mean of the Von Mises PDF.
• VON_MISES_PDF evaluates the Von Mises PDF.
• VON_MISES_SAMPLE samples the Von Mises PDF.
• WEIBULL_CDF evaluates the Weibull CDF.
• WEIBULL_CDF_INV inverts the Weibull CDF.
• WEIBULL_CHECK checks the parameters of the Weibull CDF.
• WEIBULL_MEAN returns the mean of the Weibull PDF.
• WEIBULL_PDF evaluates the Weibull PDF.
• WEIBULL_SAMPLE samples the Weibull PDF.
• WEIBULL_VARIANCE returns the variance of the Weibull PDF.
• WEIBULL_DISCRETE_CDF evaluates the Discrete Weibull CDF.
• WEIBULL_DISCRETE_CDF_INV inverts the Discrete Weibull CDF.
• WEIBULL_DISCRETE_CHECK checks the parameters of the discrete Weibull CDF.
• WEIBULL_DISCRETE_PDF evaluates the discrete Weibull PDF.
• WEIBULL_DISCRETE_SAMPLE samples the discrete Weibull PDF.
• ZETA estimates the Riemann Zeta function.
• ZIPF_CDF evaluates the Zipf CDF.
• ZIPF_CHECK checks the parameter of the Zipf PDF.
• ZIPF_MEAN returns the mean of the Zipf PDF.
• ZIPF_PDF evaluates the Zipf PDF.
• ZIPF_SAMPLE samples the Zipf PDF.
• ZIPF_VARIANCE returns the variance of the Zipf PDF.

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