# PROB Probability Density Functions

PROB is a FORTRAN77 library which handles various discrete and continuous probability density functions ("PDF's").

For a discrete variable X, PDF(X) is the probability that the value X will occur; for a continuous variable, PDF(X) is the probability density of X, that is, the probability of a value between X and X+dX is PDF(X) * dX.

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.

In some cases, the inverse of the CDF can easily be computed. If

```
X = CDF_INV ( P )
```
then we are asserting that the value X has a cumulative probability density function of P, in other words, the probability that the variable is less than or equal to X is P. If the CDF cannot be analytically inverted, there are simple ways to try to estimate the inverse. Depending on the PDF, these methods may be rapid and accurate, or not.

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 often known beforehand, and no summation or integration is required.

For many of the distributions, it is possible to repeatedly request "samples", that is, a pseudorandom sequence of realizations of the PDF. These samples are always associated with an integer seed, which controls the calculation. Using the same seed as input will guarantee the same sample value on output. Ultimately, a random number generator must be invoked internally. In most cases, the current code will call a routine called R8_UNIFORM_01, which uses a very basic, and old, random number generator. You may prefer a different random number generator for this purpose.

### Languages:

PROB is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

### Related Data and Programs:

ASA005, a FORTRAN77library which evaluates the CDF of the noncentral T distribution.

ASA066, a FORTRAN77 library which evaluates the CDF of the normal distribution.

ASA076, a FORTRAN77 library which evaluates the Owen's T function, needed to compute the CDF of the noncentral T distribution.

ASA091, a FORTRAN77 library which evaluates the percentage points of the Chi-Squared distribution.

ASA111, a FORTRAN77 library which evaluates the percentage points of the normal distribution.

ASA152, a FORTRAN77 library which evaluates point and cumulative probabilities associated with the hypergeometric distribution; this is Applied Statistics Algorithm 152;

ASA226, a FORTRAN77 library which evaluates the CDF of the noncentral Beta distribution.

ASA241, a FORTRAN77 library which evaluates the percentage points of the normal distribution.

ASA243, a FORTRAN77 library which evaluates the CDF of the noncentral T distribution.

ASA266, a FORTRAN77 library which evaluates various properties of the Dirichlet probability density function; this is Applied Statistics Algorithm 266;

ASA310, a FORTRAN77 library which computes the CDF of the noncentral Beta distribution.

BETA_NC, a FORTRAN77 library which evaluates the CDF of the noncentral Beta distribution.

CDFLIB, a FORTRAN90 library which evaluates the cumulative density function (CDF), inverse CDF, and certain other inverse functions, for distributions including beta, binomial, chi-square, noncentral chi-square, F, noncentral F, gamma, negative binomial, normal, Poisson, and students T, by Barry Brown, James Lovato, Kathy Russell.

DISCRETE_PDF_SAMPLE_2D, a FORTRAN77 program which demonstrates how to construct a Probability Density Function (PDF) from a table of sample data, and then to use that PDF to create new samples.

NORMAL, a FORTRAN77 library which samples the normal distribution.

RANLIB, a FORTRAN77 library which produces random samples from Probability Density Functions (PDF's), including Beta, Chi-square Exponential, F, Gamma, Multivariate normal, Noncentral chi-square, Noncentral F, Univariate normal, random permutations, Real uniform, Binomial, Negative Binomial, Multinomial, Poisson and Integer uniform, by Barry Brown and James Lovato.

TEST_VALUES, a FORTRAN77 library which contains sample values for a number of distributions.

TOMS441, a FORTRAN77 library which samples the dipole distribution;
this is ACM TOMS algorithm 441.

TOMS725, a FORTRAN77 library which evaluates multivariate normal integrals associated with the computation of cumulative probabilities associated with a multidimensional variable governed by a normal probability density function with a known correlation matrix, by Zvi Drezner. This is a version of ACM TOMS algorithm 725.

TRUNCATED_NORMAL, a FORTRAN77 library which works with the truncated normal distribution over [A,B], or [A,+oo) or (-oo,B], returning the probability density function (PDF), the cumulative density function (CDF), the inverse CDF, the mean, the variance, and sample values.

UNIFORM, a FORTRAN77 library which samples the uniform distribution.

ZIGGURAT, a FORTRAN77 program which generates points from a uniform, normal or exponential distribution, using the ziggurat method.

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### Source Code:

• prob.f, the source code;
• prob.sh, commands to compile the source code;

### List of Routines:

• ANGLE_CDF evaluates the Angle CDF.
• ANGLE_MEAN returns the mean of the Angle PDF.
• ANGLE_PDF evaluates the Angle PDF.
• 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_CHECK checks the parameter of 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 PDF.
• BESSEL_IX_VALUES returns some values of the Ix Bessel function.
• BIRTHDAY_CDF returns the Birthday Concurrence CDF.
• BIRTHDAY_CDF_INV inverts the Birthday Concurrence CDF.
• BIRTHDAY_PDF returns the Birthday Concurrence PDF.
• 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.
• BESSEL_I0 evaluates the modified Bessel function I0(X).
• BESSEL_I0_VALUES returns some values of the I0 Bessel function.
• BESSEL_I1 evaluates the Bessel I function of order I.
• BESSEL_I1_VALUES returns some values of the I1 Bessel function.
• 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 computes the inverse of the incomplete Beta function.
• BETA_CDF_INV_OLD inverts the Beta CDF.
• BETA_CDF_VALUES returns some values of 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_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.
• BUFFON_LAPLACE_PDF evaluates the Buffon-Laplace PDF.
• BUFFON_LAPLACE_SIMULATE simulates a Buffon-Laplace needle experiment.
• BUFFON_PDF evaluates the Buffon PDF.
• BUFFON_SIMULATE simulates a Buffon needle experiment.
• 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.
• C4_NORMAL_01_SAMPLE samples the complex Normal 01 PDF.
• CARDIOID_CDF evaluates the Cardioid CDF.
• CARDIOID_CDF_INV inverts the Cardioid CDF.
• CARDIOID_CHECK checks the parameters of the Cardioid CDF.
• CARDIOID_MEAN returns the mean of the Cardioid PDF.
• CARDIOID_PDF evaluates the Cardioid PDF.
• CARDIOID_SAMPLE samples the Cardioid PDF.
• CARDIOID_VARIANCE returns the variance of the Cardioid PDF.
• CAUCHY_CDF evaluates the Cauchy CDF.
• CAUCHY_CDF_INV inverts the Cauchy CDF.
• CAUCHY_CDF_VALUES returns some values of 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.
• CHI_SQUARE_CDF evaluates the Chi squared CDF.
• CHI_SQUARE_CDF_INV inverts the Chi squared PDF.
• CHI_SQUARE_CDF_VALUES returns some values of the Chi-Square CDF.
• CHI_SQUARE_CHECK checks the parameter of the central Chi squared PDF.
• CHI_SQUARE_MEAN returns the mean of the central Chi squared PDF.
• CHI_SQUARE_PDF evaluates the central Chi squared PDF.
• CHI_SQUARE_SAMPLE samples the central Chi squared PDF.
• CHI_SQUARE_VARIANCE returns the variance of the central Chi squared PDF.
• CHI_SQUARE_NONCENTRAL_CHECK check parameters of noncentral Chi Squared PDF.
• CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral chi CDF.
• CHI_SQUARE_NONCENTRAL_MEAN: mean of the noncentral Chi squared PDF.
• CHI_SQUARE_NONCENTRAL_SAMPLE samples the noncentral Chi squared PDF.
• CHI_SQUARE_NONCENTRAL_VARIANCE: 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: variance of the Circular Normal 01 PDF.
• CIRCULAR_NORMAL_MEAN returns the mean of the Circular Normal PDF.
• CIRCULAR_NORMAL_PDF evaluates the Circular Normal PDF.
• CIRCULAR_NORMAL_SAMPLE samples the Circular Normal PDF.
• CIRCULAR_NORMAL_VARIANCE returns the variance of the Circular Normal PDF.
• COMBINATORIAL computes the binomial coefficient C(N,K).
• 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_COMPLETE_PDF evaluates the Complete Coupon Collection PDF.
• COUPON_MEAN returns the mean of the Coupon PDF.
• COUPON_SIMULATE simulates the coupon collector's problem.
• COUPON_VARIANCE returns the variance of the Coupon PDF.
• 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.
• 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: variance of the Empirical Discrete PDF.
• ENGLISH_SENTENCE_LENGTH_CDF evaluates the English Sentence Length CDF.
• ENGLISH_SENTENCE_LENGTH_CDF_INV inverts the English Sentence Length CDF.
• ENGLISH_SENTENCE_LENGTH_MEAN: mean of the English Sentence Length PDF.
• ENGLISH_SENTENCE_LENGTH_PDF evaluates the English Sentence Length PDF.
• ENGLISH_SENTENCE_LENGTH_SAMPLE samples the English Sentence Length PDF.
• ENGLISH_SENTENCE_LENGTH_VARIANCE: variance of English Sentence Length PDF.
• ENGLISH_WORD_LENGTH_CDF evaluates the English Word Length CDF.
• ENGLISH_WORD_LENGTH_CDF_INV inverts the English Word Length CDF.
• ENGLISH_WORD_LENGTH_MEAN evaluates the mean of the English Word Length PDF.
• ENGLISH_WORD_LENGTH_PDF evaluates the English Word Length PDF.
• ENGLISH_WORD_LENGTH_SAMPLE samples the English Word Length PDF.
• ENGLISH_WORD_LENGTH_VARIANCE: variance of the English Word Length PDF.
• ERROR_F evaluates the error function ERF.
• ERROR_F_INVERSE inverts the error function ERF.
• 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.
• 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_CDF_VALUES returns some values of 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_VALUES_CDF evaluates the Extreme Values CDF.
• EXTREME_VALUES_CDF_INV inverts the Extreme Values CDF.
• EXTREME_VALUES_CDF_VALUES returns some values of the Extreme Values CDF.
• EXTREME_VALUES_CHECK checks the parameters of the Extreme Values CDF.
• EXTREME_VALUES_MEAN returns the mean of the Extreme Values PDF.
• EXTREME_VALUES_PDF evaluates the Extreme Values PDF.
• EXTREME_VALUES_SAMPLE samples the Extreme Values PDF.
• EXTREME_VALUES_VARIANCE returns the variance of the Extreme Values PDF.
• F_CDF evaluates the F central CDF.
• F_CDF_VALUES returns some values of the F CDF test function.
• F_CHECK checks the parameters of the F PDF.
• F_MEAN returns the mean of the F central PDF.
• F_PDF evaluates the F central PDF.
• F_SAMPLE samples the F central PDF.
• F_VARIANCE returns the variance of the F central PDF.
• F_NONCENTRAL_CDF_VALUES returns some values of the F CDF test function.
• F_NONCENTRAL_CHECK checks the parameters of the F noncentral 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.
• FACTORIAL_STIRLING computes Stirling's approximation to N!.
• FERMI_DIRAC_SAMPLE samples a (continuous) Fermi-Dirac distribution.
• FISHER_PDF evaluates the Fisher PDF.
• FISHER_SAMPLE samples the Fisher distribution.
• 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.
• FRECHET_CDF evaluates the Frechet CDF.
• FRECHET_CDF_INV inverts the Frechet CDF.
• FRECHET_MEAN returns the mean of the Frechet PDF.
• FRECHET_PDF evaluates the Frechet PDF.
• FRECHET_SAMPLE samples the Frechet PDF.
• FRECHET_VARIANCE returns the variance of the Frechet PDF.
• GAMMA_CDF evaluates the Gamma CDF.
• GAMMA_CDF_VALUES returns some values of the Gamma CDF.
• GAMMA_CHECK checks the parameters of the Gamma PDF.
• GAMMA_INC computes the incomplete Gamma function.
• GAMMA_INC_VALUES: values of the incomplete Gamma function.
• GAMMA_LOG calculates the natural logarithm of GAMMA ( 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_CDF_VALUES returns values of 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_CDF_VALUES returns some values of 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.
• I4_FACTORIAL returns N!.
• I4_HUGE returns a "huge" I4.
• I4_UNIFORM_AB returns a scaled pseudorandom I4.
• I4ROW_MAX returns the maximums of rows of an I4ROW.
• I4ROW_MEAN returns the means of the rows of an I4ROW.
• I4ROW_MIN returns the minimums of rows of an I4ROW.
• I4ROW_VARIANCE returns the variances of the rows of an I4ROW.
• I4VEC_MAX computes the maximum element of an I4VEC.
• I4VEC_MEAN returns the mean of an I4VEC.
• I4VEC_MIN computes the minimum element of an I4VEC.
• I4VEC_PRINT prints an I4VEC.
• I4VEC_RUN_COUNT counts runs of equal values in an I4VEC.
• I4VEC_SUM returns the sum of the entries of an I4VEC.
• I4VEC_VARIANCE returns the variance of an I4VEC.
• 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.
• LAPLACE_CDF evaluates the Laplace CDF.
• LAPLACE_CDF_INV inverts the Laplace CDF.
• LAPLACE_CDF_VALUES returns some values of 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.
• LEVY_CDF evaluates the Levy CDF.
• LEVY_CDF_INV inverts the Levy CDF.
• LEVY_PDF evaluates the Levy PDF.
• LEVY_SAMPLE samples the Levy PDF.
• LOGISTIC_CDF evaluates the Logistic CDF.
• LOGISTIC_CDF_INV inverts the Logistic CDF.
• LOGISTIC_CDF_VALUES returns some values of 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.
• LOG_NORMAL_CDF evaluates the Lognormal CDF.
• LOG_NORMAL_CDF_INV inverts the Lognormal CDF.
• LOG_NORMAL_CDF_VALUES returns some values of the Log Normal CDF.
• LOG_NORMAL_CHECK checks the parameters of the Lognormal PDF.
• LOG_NORMAL_MEAN returns the mean of the Lognormal PDF.
• LOG_NORMAL_PDF evaluates the Lognormal PDF.
• LOG_NORMAL_SAMPLE samples the Lognormal PDF.
• LOG_NORMAL_VARIANCE returns the variance of the Lognormal PDF.
• LOG_SERIES_CDF evaluates the Logarithmic Series CDF.
• LOG_SERIES_CDF_INV inverts the Logarithmic Series CDF.
• LOG_SERIES_CDF_VALUES returns some values of the log series CDF.
• LOG_SERIES_CHECK checks the parameter of the Logarithmic Series PDF.
• LOG_SERIES_MEAN returns the mean of the Logarithmic Series PDF.
• LOG_SERIES_PDF evaluates the Logarithmic Series PDF.
• LOG_SERIES_SAMPLE samples the Logarithmic Series PDF.
• LOG_SERIES_VARIANCE returns the variance of the Logarithmic Series PDF.
• LOG_UNIFORM_CDF evaluates the Log Uniform CDF.
• LOG_UNIFORM_CDF_INV inverts the Log Uniform CDF.
• LOG_UNIFORM_CHECK checks the parameters of the Log Uniform CDF.
• LOG_UNIFORM_MEAN returns the mean of the Log Uniform PDF.
• LOG_UNIFORM_PDF evaluates the Log Uniform PDF.
• LOG_UNIFORM_SAMPLE samples the Log Uniform 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.
• NEGATIVE_BINOMIAL_CDF evaluates the Negative Binomial CDF.
• NEGATIVE_BINOMIAL_CDF_INV inverts the Negative Binomial CDF.
• NEGATIVE_BINOMIAL_CDF_VALUES returns values of the negative binomial CDF.
• NEGATIVE_BINOMIAL_CHECK checks the parameters of the Negative Binomial PDF.
• NEGATIVE_BINOMIAL_MEAN returns the mean of the Negative Binomial PDF.
• NEGATIVE_BINOMIAL_PDF evaluates the Negative Binomial PDF.
• NEGATIVE_BINOMIAL_SAMPLE samples the Negative Binomial PDF.
• NEGATIVE_BINOMIAL_VARIANCE returns the variance of the Negative Binomial PDF.
• NORMAL_01_CDF evaluates the Normal 01 CDF.
• NORMAL_01_CDF_INV inverts the standard normal CDF.
• NORMAL_01_CDF_VALUES returns some values of 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 probability distribution.
• NORMAL_01_VARIANCE returns the variance of the Normal 01 PDF.
• NORMAL_01_VECTOR samples the standard normal probability distribution.
• NORMAL_CDF evaluates the Normal CDF.
• NORMAL_CDF_INV inverts the Normal CDF.
• NORMAL_CDF_VALUES returns some values of 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.
• NORMAL_VECTOR samples the normal probability distribution.
• NORMAL_TRUNCATED_AB_CDF evaluates the truncated Normal CDF.
• NORMAL_TRUNCATED_AB_CDF_INV inverts the truncated Normal CDF.
• NORMAL_TRUNCATED_AB_MEAN returns the mean of the truncated Normal PDF.
• NORMAL_TRUNCATED_AB_PDF evaluates the truncated Normal PDF.
• NORMAL_TRUNCATED_AB_SAMPLE samples the truncated Normal PDF.
• NORMAL_TRUNCATED_AB_VARIANCE returns the variance of the truncated Normal PDF.
• NORMAL_TRUNCATED_A_CDF evaluates the lower truncated Normal CDF.
• NORMAL_TRUNCATED_A_CDF_INV inverts the lower truncated Normal CDF.
• NORMAL_TRUNCATED_A_MEAN returns the mean of the lower truncated Normal PDF.
• NORMAL_TRUNCATED_A_PDF evaluates the lower truncated Normal PDF.
• NORMAL_TRUNCATED_A_SAMPLE samples the lower truncated Normal PDF.
• NORMAL_TRUNCATED_A_VARIANCE: variance of the lower truncated Normal PDF.
• NORMAL_TRUNCATED_B_CDF evaluates the upper truncated Normal CDF.
• NORMAL_TRUNCATED_B_CDF_INV inverts the upper truncated Normal CDF.
• NORMAL_TRUNCATED_B_MEAN returns the mean of the upper truncated Normal PDF.
• NORMAL_TRUNCATED_B_PDF evaluates the upper truncated Normal PDF.
• NORMAL_TRUNCATED_B_SAMPLE samples the upper truncated Normal PDF.
• NORMAL_TRUNCATED_B_VARIANCE: variance of the upper truncated Normal PDF.
• OWEN_VALUES returns some values of Owen's T function.
• 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.
• 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.
• PLANCK_CHECK checks the parameters of the Planck PDF.
• 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.
• POINT_DISTANCE_1D_PDF evaluates the point distance PDF in 1D.
• POINT_DISTANCE_2D_PDF evaluates the point distance PDF in 2D.
• POINT_DISTANCE_3D_PDF evaluates the point distance PDF in the 3D.
• 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_KERNEL evaluates the Poisson kernel.
• POISSON_PDF evaluates the Poisson PDF.
• POISSON_SAMPLE samples the Poisson PDF.
• POISSON_VARIANCE returns the variance of the Poisson PDF.
• 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.
• PSI_VALUES returns some values of the Psi or Digamma function for testing.
• QUASIGEOMETRIC_CDF evaluates the Quasigeometric CDF.
• QUASIGEOMETRIC_CDF_INV inverts the Quasigeometric CDF.
• QUASIGEOMETRIC_CHECK checks the parameters of the Quasigeometric CDF.
• QUASIGEOMETRIC_MEAN returns the mean of the Quasigeometric PDF.
• QUASIGEOMETRIC_PDF evaluates the Quasigeometric PDF.
• QUASIGEOMETRIC_SAMPLE samples the Quasigeometric PDF.
• QUASIGEOMETRIC_VARIANCE returns the variance of the Quasigeometric PDF.
• R4_UNIFORM_AB returns a scaled real pseudorandom number.
• R4_UNIFORM_01 returns a unit real pseudorandom number.
• R8_CEILING rounds an R8 "up" to the nearest integral R8.
• R8_CSC returns the cosecant of X.
• R8_EPSILON returns the R8 roundoff unit.
• R8_GAMMA evaluates Gamma(X) for a real argument.
• R8_HUGE returns a "huge" R8.
• R8_IS_INT determines if an R8 represents an integer value.
• R8_PI returns the value of pi to 16 decimal places.
• R8_UNIFORM_AB returns a scaled pseudorandom R8.
• R8_UNIFORM_01 returns a unit pseudorandom R8.
• R8MAT_PRINT prints an R8MAT.
• R8MAT_PRINT_SOME prints some of an R8MAT.
• R8POLY_VALUE evaluates an R8POLY
• R8ROW_MAX returns the maximums of rows of an R8ROW.
• R8ROW_MEAN returns the means of an R8ROW.
• R8ROW_MIN returns the minimums of rows of an R8ROW.
• R8ROW_VARIANCE returns the variances of an R8ROW.
• R8VEC_CIRCULAR_VARIANCE returns the circular variance of an R8VEC.
• R8VEC_DIFF_NORM returns the L2 norm of the difference of R8VEC's.
• R8VEC_DOT_PRODUCT finds the dot product of a pair of R8VEC's.
• R8VEC_MAX returns the maximum value in an R8VEC.
• R8VEC_MEAN returns the mean of an R8VEC.
• R8VEC_MIN returns the minimum value of an R8VEC.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_SUM sums the entries of an R8VEC.
• R8VEC_UNIFORM_AB returns a scaled pseudorandom R8VEC.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• R8VEC_UNIT_SUM normalizes an R8VEC to have unit sum.
• R8VEC_VARIANCE returns the variance of an R8VEC.
• RAYLEIGH_CDF evaluates the Rayleigh CDF.
• RAYLEIGH_CDF_INV inverts the Rayleigh CDF.
• RAYLEIGH_CDF_VALUES returns some values of 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.
• RIBESL calculates I Bessel function with non-integer orders.
• RUNS_MEAN returns the mean of the Runs PDF.
• RUNS_PDF evaluates the Runs PDF.
• RUNS_SAMPLE samples the Runs PDF.
• RUNS_SIMULATE simulates a case governed by the Runs PDF.
• RUNS_VARIANCE returns the variance of the Runs PDF.
• 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.
• SIN_POWER_INT evaluates the sine power integral.
• SPHERE_UNIT_AREA_ND computes the surface area of a unit sphere in ND.
• STIRLING2_VALUE computes a Stirling number of the second kind.
• STUDENT_CDF evaluates the central Student T CDF.
• STUDENT_CDF_VALUES returns some values of the Student CDF.
• STUDENT_CHECK checks the parameter of the central Student T CDF.
• STUDENT_MEAN returns the mean of the central Student T PDF.
• STUDENT_PDF evaluates the central Student T PDF.
• STUDENT_SAMPLE samples the central Student T PDF.
• STUDENT_VARIANCE returns the variance of the central Student T PDF.
• STUDENT_NONCENTRAL_CDF evaluates the noncentral Student T CDF.
• STUDENT_NONCENTRAL_CDF_VALUES returns values of the noncentral Student CDF.
• TFN calculates the T function of Owen.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• TRIANGLE_CDF evaluates the Triangle CDF.
• TRIANGLE_CDF_INV inverts the Triangle CDF.
• TRIANGLE_CHECK checks the parameters of the Triangle CDF.
• TRIANGLE_MEAN returns the mean of the Triangle PDF.
• TRIANGLE_PDF evaluates the Triangle PDF.
• TRIANGLE_SAMPLE samples the Triangle PDF.
• TRIANGLE_VARIANCE returns the variance of the Triangle PDF.
• 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 the TriGamma function.
• 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_CDF_VALUES returns some values of the von Mises CDF.
• VON_MISES_CHECK checks the parameters of the von Mises PDF.
• VON_MISES_CIRCULAR_VARIANCE: circular variance 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_CDF_VALUES returns some values of 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.

You can go up one level to the FORTRAN77 source codes.

Last revised on 21 August 2013.