Chapter 18: Random Number Generation

Routines

Utility Routines for Random Number Generators

Selects the uniform (0,1) generator........................................................................ RNOPT

Retrieves the indicator of the generator currently used............................................ RNOPG

Initializes the seed used in the generators.............................................................. RNSET

Retrieves the current value of the seed................................................................... RNGET

Initializes the table used in the shuffled generators.................................................. RNSES

Retrieves the current table used in the shuffled
generators.......................................................................................................... RNGES

Initializes the table used in the GFSR generator...................................................... RNSEF

Retrieves the current table used in the GFSR generator........................................... RNGEF

Get a seed for a separate substream of numbers..................................................... RNISD

Initializes the 32-bit Mersenne Twister generator
using an array...................................................................................................... RNIN32

Retrieves the current table used in the 32-bit
Mersenne Twister generator................................................................................ RNGE32

Sets the current table used in the 32-bit
Mersenne Twister generator................................................................................. RNSE32

Initializes the 64-bit Mersenne Twister generator
using an array...................................................................................................... RNIN64

Retrieves the current table used in the 64-bit
Mersenne Twister generator................................................................................ RNGE64

Sets the current table used in the 64-bit
Mersenne Twister generator................................................................................. RNSE64

Basic Uniform Distribution

Uniform (0,1).......................................................................................................... RNUN

Uniform (0,1), function form................................................................................... RNUNF

Univariate Discrete Distributions

Binomial............................................................................................................... RNBIN

General discrete distribution, using alias method.................................................... RNGDA

General discrete distribution, set up table.............................................................. RNGDS

General discrete distribution, using table lookup..................................................... RNGDT

Geometric.......................................................................................................... RNGEO

Hypergeometric................................................................................................... RNHYP

Logarithmic......................................................................................................... RNLGR

Negative binomial................................................................................................. RNNBN

Poisson............................................................................................................... RNPOI

Discrete uniform.................................................................................................. RNUND

Univariate Continuous Distributions

Beta.................................................................................................................... RNBET

Chi-squared.......................................................................................................... RNCHI

Cauchy............................................................................................................... RNCHY

Exponential......................................................................................................... RNEXP

Extreme value...................................................................................................... RNEXV

F........................................................................................................................ RNFDF

Mixture of two exponentials................................................................................... RNEXT

Gamma.............................................................................................................. RNGAM

General continuous distribution, set up table.......................................................... RNGCS

General continuous distribution, using table lookup................................................. RNGCT

Lognormal............................................................................................................ RNLNL

Normal, using acceptance/rejection                                                                RNNOA

Normal, function form of RNNOR........................................................................... RNNOF

Normal, using inverse CDF................................................................................... RNNOR

Rayleigh.............................................................................................................. RNRAL

Stable................................................................................................................. RNSTA

Student’s t........................................................................................................... RNSTT

Triangular.............................................................................................................. RNTRI

Von Mises.......................................................................................................... RNVMS

Weibull................................................................................................................ RNWIB

Multivariate Distributions

Orthogonal matrices and correlation matrices......................................................... RNCOR

Data-based multivariate......................................................................................... RNDAT

Multinomial......................................................................................................... RNMTN

Multivariate normal.............................................................................................. RNMVN

Points on a unit circle or sphere............................................................................ RNSPH

Two-way tables.................................................................................................... RNTAB

Multivariate Gaussian Copula............................................................................. RNMVGC

Multivariate Student’s t Copula............................................................................ RNMVTC

Canonical Correlation......................................................................................... CANCOR

Order Statistics

Order statistics from a normal distribution.............................................................. RNNOS

Order statistics from a uniform distribution............................................................. RNUNO

Stochastic Processes

ARMA process................................................................................................... RNARM

Nonhomogeneous Poisson process....................................................................... RNNPP

Samples and Permutations

Random permutation............................................................................................ RNPER

Random sample of indices..................................................................................... RNSRI

Random sample.................................................................................................. RNSRS

Low Discrepancy Sequences

Shuffled Faure sequence initialization............................................................. FAURE_INIT

Frees the structure containing information
about the Faure sequence.......................................................................... FAURE_FREE

Computes a shuffled Faure sequence........................................................... FAURE_NEXT



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