# random

Random numbers

## Description

R = random(name,A) returns a random number from the one-parameter distribution family specified by name and the distribution parameter A.

example

R = random(name,A,B) returns a random number from the two-parameter distribution family specified by name and the distribution parameters A and B.

R = random(name,A,B,C) returns a random number from the three-parameter distribution family specified by name and the distribution parameters A, B, and C.

R = random(name,A,B,C,D) returns a random number from the four-parameter distribution family specified by name and the distribution parameters A, B, C, and D.

example

R = random(pd) returns a random number from the probability distribution object pd.

example

R = random(___,sz1,...,szN) generates an array of random numbers from the specified probability distribution using input arguments from any of the previous syntaxes, where sz1,...,szN indicates the size of each dimension.

example

R = random(___,sz) generates an array of random numbers from the specified probability distribution using input arguments from any of the previous syntaxes, where vector sz specifies size(r).

## Examples

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Generate one random number from the normal distribution with the mean $\mu$ equal to 1 and the standard deviation $\sigma$ equal to 5. Specify the distribution name 'Normal' and the distribution parameters.

rng('default') % For reproducibility
mu = 1;
sigma = 5;
r = random('Normal',mu,sigma)
r = 3.6883

Create a normal distribution object and generate one random number using the object.

Create a normal distribution object with the mean $\mu$ equal to 1 and the standard deviation $\sigma$ equal to 5.

mu = 1;
sigma = 5;
pd = makedist('Normal','mu',mu,'sigma',sigma);

Generate one random number from the distribution.

rng('default') % For reproducibility
r = random(pd)
r = 3.6883

Save the current state of the random number generator. Then generate a random number from the Poisson distribution with rate parameter 5.

s = rng;
r = random('Poisson',5)
r = 5

Restore the state of the random number generator to s, and then create a new random number. The value is the same as before.

rng(s);
r1 = random('Poisson',5)
r1 = 5

Create a matrix of random numbers with the same size as an existing array. Use the stable distribution with shape parameters 2 and 0, scale parameter 1, and location parameter 0.

A = [3 2; -2 1];
sz = size(A);
R = random('Stable',2,0,1,0,sz)
R = 2×2

0.7604   -3.1945
2.5935    1.2193

You can combine the previous two lines of code into a single line.

R = random('Stable',2,0,1,0,size(A))
R = 2×2

0.4508   -0.6132
-1.8494    0.4845

Create a Weibull probability distribution object using the default parameter values.

pd = makedist('Weibull')
pd =
WeibullDistribution

Weibull distribution
A = 1
B = 1

Generate random numbers from the distribution.

rng('default')  % For reproducibility
r = random(pd,10000,1);

Construct a histogram using 100 bins with a Weibull distribution fit.

histfit(r,100,'weibull')

Create a standard normal probability distribution object.

pd = makedist('Normal')
pd =
NormalDistribution

Normal distribution
mu = 0
sigma = 1

Generate a 2-by-3-by-2 array of random numbers from the distribution.

r = random(pd,[2,3,2])
r =
r(:,:,1) =

0.5377   -2.2588    0.3188
1.8339    0.8622   -1.3077

r(:,:,2) =

-0.4336    3.5784   -1.3499
0.3426    2.7694    3.0349

## Input Arguments

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Probability distribution name, specified as one of the probability distribution names in this table.

nameDistributionInput Parameter AInput Parameter BInput Parameter CInput Parameter D
'Beta'Beta Distributiona first shape parameterb second shape parameter
'Binomial'Binomial Distributionn number of trialsp probability of success for each trial
'BirnbaumSaunders'Birnbaum-Saunders Distributionβ scale parameterγ shape parameter
'Burr'Burr Type XII Distributionα scale parameterc first shape parameterk second shape parameter
'Chisquare' or 'chi2'Chi-Square Distributionν degrees of freedom
'Exponential'Exponential Distributionμ mean
'Extreme Value' or 'ev'Extreme Value Distributionμ location parameterσ scale parameter
'F'F Distributionν1 numerator degrees of freedomν2 denominator degrees of freedom
'Gamma'Gamma Distributiona shape parameterb scale parameter
'Generalized Extreme Value' or 'gev'Generalized Extreme Value Distributionk shape parameterσ scale parameterμ location parameter
'Generalized Pareto' or 'gp'Generalized Pareto Distributionk tail index (shape) parameterσ scale parameterμ threshold (location) parameter
'Geometric'Geometric Distributionp probability parameter
'Half Normal' or 'hn'Half-Normal Distributionμ location parameterσ scale parameter
'Hypergeometric' or 'hyge'Hypergeometric Distributionm size of the populationk number of items with the desired characteristic in the populationn number of samples drawn
'InverseGaussian'Inverse Gaussian Distributionμ scale parameterλ shape parameter
'Logistic'Logistic Distributionμ meanσ scale parameter
'LogLogistic'Loglogistic Distributionμ mean of logarithmic valuesσ scale parameter of logarithmic values
'LogNormal'Lognormal Distributionμ mean of logarithmic valuesσ standard deviation of logarithmic values
'Nakagami'Nakagami Distributionμ shape parameterω scale parameter
'Negative Binomial' or 'nbin'Negative Binomial Distributionr number of successesp probability of success in a single trial
'Noncentral F' or 'ncf'Noncentral F Distributionν1 numerator degrees of freedomν2 denominator degrees of freedomδ noncentrality parameter
'Noncentral t' or 'nct'Noncentral t Distributionν degrees of freedomδ noncentrality parameter
'Noncentral Chi-square' or 'ncx2'Noncentral Chi-Square Distributionν degrees of freedomδ noncentrality parameter
'Normal'Normal Distributionμ mean σ standard deviation
'Poisson'Poisson Distributionλ mean
'Rayleigh'Rayleigh Distributionb scale parameter
'Rician'Rician Distributions noncentrality parameterσ scale parameter
'Stable'Stable Distributionα first shape parameterβ second shape parameterγ scale parameterδ location parameter
'T'Student's t Distributionν degrees of freedom
'tLocationScale't Location-Scale Distributionμ location parameterσ scale parameterν shape parameter
'Uniform'Uniform Distribution (Continuous)a lower endpoint (minimum)b upper endpoint (maximum)
'Discrete Uniform' or 'unid'Uniform Distribution (Discrete)n maximum observable value
'Weibull' or 'wbl'Weibull Distributiona scale parameterb shape parameter

Example: 'Normal'

First probability distribution parameter, specified as a scalar value or an array of scalar values.

If one or more of the input arguments A, B, C, and D are arrays, then the array sizes must be the same. In this case, random expands each scalar input into a constant array of the same size as the array inputs. See name for the definitions of A, B, C, and D for each distribution.

Data Types: single | double

Second probability distribution parameter, specified as a scalar value or an array of scalar values.

If one or more of the input arguments A, B, C, and D are arrays, then the array sizes must be the same. In this case, random expands each scalar input into a constant array of the same size as the array inputs. See name for the definitions of A, B, C, and D for each distribution.

Data Types: single | double

Third probability distribution parameter, specified as a scalar value or an array of scalar values.

If one or more of the input arguments A, B, C, and D are arrays, then the array sizes must be the same. In this case, random expands each scalar input into a constant array of the same size as the array inputs. See name for the definitions of A, B, C, and D for each distribution.

Data Types: single | double

Fourth probability distribution parameter, specified as a scalar value or an array of scalar values.

If one or more of the input arguments A, B, C, and D are arrays, then the array sizes must be the same. In this case, random expands each scalar input into a constant array of the same size as the array inputs. See name for the definitions of A, B, C, and D for each distribution.

Data Types: single | double

Probability distribution, specified as one of the probability distribution objects in this table.

Distribution ObjectFunction or App to Create Probability Distribution Object
BinomialDistributionmakedist, fitdist, Distribution Fitter
BirnbaumSaundersDistributionmakedist, fitdist, Distribution Fitter
BurrDistributionmakedist, fitdist, Distribution Fitter
ExponentialDistributionmakedist, fitdist, Distribution Fitter
ExtremeValueDistributionmakedist, fitdist, Distribution Fitter
GeneralizedExtremeValueDistributionmakedist, fitdist, Distribution Fitter
GeneralizedParetoDistributionmakedist, fitdist, Distribution Fitter
HalfNormalDistributionmakedist, fitdist, Distribution Fitter
InverseGaussianDistributionmakedist, fitdist, Distribution Fitter
KernelDistributionfitdist, Distribution Fitter
LogisticDistributionmakedist, fitdist, Distribution Fitter
LoglogisticDistributionmakedist, fitdist, Distribution Fitter
LognormalDistributionmakedist, fitdist, Distribution Fitter
LoguniformDistributionmakedist
MultinomialDistributionmakedist
NakagamiDistributionmakedist, fitdist, Distribution Fitter
NegativeBinomialDistributionmakedist, fitdist, Distribution Fitter
NormalDistributionmakedist, fitdist, Distribution Fitter
Piecewise distribution with generalized Pareto distributions in the tailsparetotails
PiecewiseLinearDistributionmakedist
PoissonDistributionmakedist, fitdist, Distribution Fitter
RayleighDistributionmakedist, fitdist, Distribution Fitter
RicianDistributionmakedist, fitdist, Distribution Fitter
StableDistributionmakedist, fitdist, Distribution Fitter
tLocationScaleDistributionmakedist, fitdist, Distribution Fitter
TriangularDistributionmakedist
UniformDistributionmakedist
WeibullDistributionmakedist, fitdist, Distribution Fitter

Size of each dimension, specified as integer values. For example, specifying 5,3,2 generates a 5-by-3-by-2 array of random numbers from the specified probability distribution.

If one or more of the input arguments A, B, C, and D are arrays, then the specified dimensions sz1,...,szN must match the common dimensions of A, B, C, and D after any necessary scalar expansion. The default values of sz1,...,szN are the common dimensions.

• If you specify a single value sz1, then R is a square matrix of size sz1-by-sz1.

• If the size of any dimension is 0 or negative, then R is an empty array.

• Beyond the second dimension, random ignores trailing dimensions with a size of 1. For example, specifying 3,1,1,1 produces a 3-by-1 vector of random numbers.

Example: 5,3,2

Data Types: single | double

Size of each dimension, specified as a row vector of integers. For example, specifying [5 3 2] generates a 5-by-3-by-2 array of random numbers from the specified probability distribution.

If one or more of the input arguments A, B, C, and D are arrays, then the specified dimensions sz must match the common dimensions of A, B, C, and D after any necessary scalar expansion. The default values of sz are the common dimensions.

• If you specify a single value [sz1], then R is a square matrix of size sz1-by-sz1.

• If the size of any dimension is 0 or negative, then R is an empty array.

• Beyond the second dimension, random ignores trailing dimensions with a size of 1. For example, specifying [3 1 1 1] produces a 3-by-1 vector of random numbers.

Example: [5 3 2]

Data Types: single | double

## Output Arguments

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Random number generated from the specified probability distribution, returned as a scalar value or an array of scalar values with the dimensions specified by sz1,...,szN or sz.

If you specify distribution parameters A, B, C, or D, then each element in R is the random number generated from the distribution specified by the corresponding elements in A, B, C, and D.

## Alternative Functionality

• random is a generic function that accepts either a distribution by its name name or a probability distribution object pd. It is faster to use a distribution-specific function, such as randn and normrnd for the normal distribution and binornd for the binomial distribution. For a list of distribution-specific functions, see Supported Distributions.

• To generate random numbers interactively, use randtool, a user interface for random number generation.