RANLIB
General Random Number Generators (RNG's)

RANLIB, a MATLAB 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.

RANLIB relies on streams of uniform random numbers generated by a lower level package called RNGLIB. A copy of RNGLIB must be available in order for RANLIB to executed. The RNGLIB routines provide 32 virtual random number generators. Each generator can provide 1,048,576 blocks of numbers, and each block is of length 1,073,741,824. Any generator can be set to the beginning or end of the current block or to its starting value. Packaging is provided so that if these capabilities are not needed, a single generator with period 2.3 X 10^18 is seen.

The routines, and the probability density functions they sample, include:

• GENBET, Beta distribution;
• GENCHI, Chi-Square distribution;
• GENEXP, Exponential distribution;
• GENF, F distribution;
• GENGAM, Gamma distribution;
• GENMN, multivariate normal distribution;
• GENMUL, multinomial distribution;
• GENNCH, noncentral Chi-Square distribution;
• GENNF, noncentral F distribution;
• GENNOR, normal distribution;
• GENUNF, uniform distribution on [0,1];
• IGNBIN, binomial distribution;
• IGNLGI, uniform distribution on integers between 1 and 2147483562;
• IGNNBN, negative binomial distribution.
• IGNPOI, Poisson distribution.
• IGNUIN, uniform distribution on integers in a given range.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

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

Related Data and Programs:

ASA183, a MATLAB library which implements a random number generator (RNG), by Wichman and Hill. This is a MATLAB version of Applied Statistics Algorithm 183.

FAURE, a MATLAB library which computes elements of a Faure quasirandom sequence.

HALTON, a MATLAB library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY, a MATLAB library which computes elements of a Hammersley quasirandom sequence.

NIEDERREITER2, a MATLAB library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL, a MATLAB library which computes elements of a sequence of pseudorandom normally distributed values.

PDFLIB, a MATLAB library which evaluates Probability Density Functions (PDF's) and produces random samples from them, including beta, binomial, chi, exponential, gamma, inverse chi, inverse gamma, multinomial, normal, scaled inverse chi, and uniform.

PROB, a MATLAB library which evaluates, samples and inverts a number of Probability Density Functions (PDF's).

RANDOM_SORTED, a MATLAB library which generates vectors of random values which are already sorted.

ranlib_test

RNGLIB, a MATLAB library which implements a random number generator (RNG) with splitting facilities, allowing multiple independent streams to be computed, by L'Ecuyer and Cote.

SOBOL, a MATLAB library which computes elements of a Sobol quasirandom sequence.

UNIFORM, a MATLAB library which computes elements of a pseudorandom uniform sequence.

VAN_DER_CORPUT, a MATLAB library which computes elements of a van der Corput quasirandom sequence.

WALKER_SAMPLE, a MATLAB library which efficiently samples a discrete probability vector using Walker sampling.

Author:

Original FORTRAN77 version by Barry Brown, James Lovato. MATLAB version by John Burkardt.

Reference:

1. Joachim Ahrens, Ulrich Dieter,
   Computer Methods for Sampling From the Exponential and Normal Distributions,
   Communications of the ACM,
   Volume 15, Number 10, October 1972, pages 873-882.
2. Joachim Ahrens, Ulrich Dieter,
   Generating Gamma Variates by a Modified Rejection Technique,
   Communications of the ACM,
   Volume 25, Number 1, January 1982, pages 47-54.
3. Joachim Ahrens, Ulrich Dieter,
   Computer Generation of Poisson Deviates From Modified Normal Distributions,
   ACM Transactions on Mathematical Software,
   Volume 8, Number 2, June 1982, pages 163-179.
4. Joachim Ahrens, Ulrich Dieter,
   Computer Methods for Sampling from Gamma, Beta, Poisson and Binomial Distributions,
   Computing,
   Volume 12, Number 3, September 1974, pages 223-246.
5. Joachim Ahrens, Ulrich Dieter,
   Extensions of Forsythe's Method for Random Sampling from the Normal Distribution,
   Mathematics of Computation,
   Volume 27, Number 124, October 1973, page 927-937.
6. Russell Cheng,
   Generating Beta Variates with Nonintegral Shape Parameters,
   Communications of the ACM,
   Volume 21, Number 4, April 1978, pages 317-322.
7. Luc Devroye,
   Non-Uniform Random Variate Generation,
   Springer, 1986,
   ISBN: 0387963057,
   LC: QA274.D48.
8. Voratas Kachitvichyanukul, Bruce Schmeiser,
   Binomial Random Variate Generation,
   Communications of the ACM,
   Volume 31, Number 2, February 1988, page 216-222.
9. Pierre LEcuyer, Serge Cote,
   Implementing a Random Number Package with Splitting Facilities,
   ACM Transactions on Mathematical Software,
   Volume 17, Number 1, March 1991, pages 98-111.

Source Code:

• genbet.m, generates a beta random deviate.
• genchi.m, generates a Chi-Square random deviate.
• genexp.m, generates an exponential random deviate.
• genf.m, generates an F random deviate.
• gengam.m, generates a Gamma random deviate.
• genmn.m, generates a multivariate normal deviate.
• genmul.m, generates a multinomial random deviate.
• gennch.m, generates a noncentral Chi-Square random deviate.
• gennf.m, generates a noncentral F random deviate.
• gennor.m, generates a normal random deviate.
• genprm.m, generates and applies a random permutation to an array.
• genunf.m, generates a uniform random deviate.
• ignbin.m, generates a binomial random deviate.
• ignnbn.m, generates a negative binomial random deviate.
• ignpoi.m, generates a Poisson random deviate.
• ignuin.m, generates a random integer in a given range.
• lennob.m, counts the length of a string, ignoring trailing blanks.
• phrtsd.m, converts a phrase to a pair of random number generator seeds.
• phrtsd_test.m
• prcomp.m, prints covariance information.
• r4_exp.m, evaluates the exponential function while avoiding overflow and underflow.
• r4_exponential_sample.m, samples an exponential distribution.
• r4vec_covar.m, computes the covariance of two R4VEC's.
• r8_exponential_sample.m, samples an exponential distribution.
• r8vec_covar.m, computes the covariance of two R8VEC's.
• setcov.m, sets a covariance matrix from variance and common correlation.
• setgmn.m, sets data for the generation of multivariate normal deviates.
• sexpo.m, evaluates the standard exponential distribution.
• sgamma.m, returns a deviate from the standard Gamma distribution.
• snorm.m, returns a deviate from the standard normal distribution.
• snorm_test.m
• spofa.m, factors a real symmetric positive definite matrix.
• stats.m, computes statistics for a given array.
• trstat.m, returns the mean and variance for distributions.