Random Number Generation

Statistics and Machine Learning Toolbox™ supports the generation of random numbers from various distributions. Each random number generator (RNG) represents a parametric family of distributions. RNGs return random numbers from the specified distribution in an array of the specified dimensions.

Other random number generation functions which do not support specific distributions include:

• cvpartition

• datasample

• hmmgenerate

• lhsdesign

• lhsnorm

• mhsample

• random

• randsample

• slicesample

• hmcSampler

RNGs in Statistics and Machine Learning Toolbox software depend on the default random number stream of MATLAB^® via the rand and randn functions. Each RNG uses one of the techniques discussed in Common Pseudorandom Number Generation Methods to generate random numbers from a given distribution.

By controlling the default random number stream and its state, you can control how the RNGs in Statistics and Machine Learning Toolbox software generate random values. For example, to reproduce the same sequence of values from an RNG, you can save and restore the default stream's state, or reset the default stream. For details on managing the default random number stream, see Managing the Global Stream Using RandStream.

MATLAB initializes the default random number stream to the same state each time it starts up. Thus, RNGs in Statistics and Machine Learning Toolbox software will generate the same sequence of values for each MATLAB session unless you modify that state at startup. One simple way to do that is to add commands to startup.m such as

rng shuffle

that initialize the default random number stream to a different state for each session.

The following table lists the supported distributions and their respective random number generation functions.

Distribution	Random Number Generation Function
Beta	betarnd, random, randtool
Binomial	binornd, random, randtool
Birnbaum-Saunders	random
Burr Type XII	random, randtool
Chi-square	chi2rnd, random, randtool
Clayton copula	copularnd
Exponential	exprnd, random, randtool
Extreme value	evrnd, random, randtool
F	frnd, random, randtool
Frank copula	copularnd
Gamma	gamrnd, randg, random, randtool
Gaussian copula	copularnd
Gaussian Mixture	random
Generalized extreme value	gevrnd, random, randtool
Generalized Pareto	gprnd, random, randtool
Geometric	geornd, random, randtool
Gumbel copula	copularnd
Half-Normal	random, randtool
Hypergeometric	hygernd, random, randtool
Inverse Gaussian	random
Inverse Wishart	iwishrnd
Johnson system	johnsrnd
Kernel	random
Logistic	random
Loglogistic	random
Lognormal	lognrnd, random, randtool
Multinomial	mnrnd
Multivariate normal	mvnrnd
Multivariate t	mvtrnd
Nakagami	random
Negative binomial	nbinrnd, random, randtool
Noncentral chi-square	ncx2rnd, random, randtool
Noncentral F	ncfrnd, random, randtool
Noncentral t	nctrnd, random, randtool
Normal (Gaussian)	normrnd, randn, random, randtool
Pareto	random
Pearson system	pearsrnd
Piecewise	random
Poisson	poissrnd, random, randtool
Rayleigh	raylrnd, random, randtool
Rician	random
Stable	random
Student's t	trnd, random, randtool
t copula	copularnd
t location- scale	random
Triangular	random
Uniform (continuous)	unifrnd, rand, random
Uniform (discrete)	unidrnd, random, randtool
Weibull	wblrnd, random
Wishart	wishrnd

Related Topics

• Generate Random Numbers Using the Triangular Distribution
• Generate Random Numbers Using Uniform Distribution Inversion
• Generating Pseudorandom Numbers
• Generating Quasi-Random Numbers
• Working with Probability Distributions
• Supported Distributions