random
Random numbers
Syntax
Description
generates an array of random numbers from the specified probability distribution
using input arguments from any of the previous syntaxes, where
R
= random(___,sz1,...,szN
)sz1,...,szN
indicates the size of each
dimension.
Examples
Generate One Random Number by Specifying Distribution Name and Parameters
Generate one random number from the normal distribution with the mean equal to 1 and the standard deviation 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
Generate One Random Number Using Distribution Object
Create a normal distribution object and generate one random number using the object.
Create a normal distribution object with the mean equal to 1 and the standard deviation 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
Reset Random Number Generator
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
Clone Size from Existing Array
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
Generate Multiple Random Numbers
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')
Generate Multidimensional Array of Random Numbers
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
name
— Probability distribution name
character vector or string scalar of probability distribution
name
Probability distribution name, specified as one of the probability distribution names in this table.
name | Distribution | Input Parameter A | Input Parameter B | Input Parameter C | Input Parameter D |
---|---|---|---|---|---|
'Beta' | Beta Distribution | a first shape parameter | b second shape parameter | — | — |
'Binomial' | Binomial Distribution | n number of trials | p probability of success for each trial | — | — |
'BirnbaumSaunders' | Birnbaum-Saunders Distribution | β scale parameter | γ shape parameter | — | — |
'Burr' | Burr Type XII Distribution | α scale parameter | c first shape parameter | k second shape parameter | — |
'Chisquare' or
'chi2' | Chi-Square Distribution | ν degrees of freedom | — | — | — |
'Exponential' | Exponential Distribution | μ mean | — | — | — |
'Extreme Value' or
'ev' | Extreme Value Distribution | μ location parameter | σ scale parameter | — | — |
'F' | F Distribution | ν1 numerator degrees of freedom | ν2 denominator degrees of freedom | — | — |
'Gamma' | Gamma Distribution | a shape parameter | b scale parameter | — | — |
'Generalized Extreme Value' or
'gev' | Generalized Extreme Value Distribution | k shape parameter | σ scale parameter | μ location parameter | — |
'Generalized Pareto' or
'gp' | Generalized Pareto Distribution | k tail index (shape) parameter | σ scale parameter | μ threshold (location) parameter | — |
'Geometric' | Geometric Distribution | p probability parameter | — | — | — |
'Half Normal' or
'hn' | Half-Normal Distribution | μ location parameter | σ scale parameter | — | — |
'Hypergeometric' or
'hyge' | Hypergeometric Distribution | m size of the population | k number of items with the desired characteristic in the population | n number of samples drawn | — |
'InverseGaussian' | Inverse Gaussian Distribution | μ scale parameter | λ shape parameter | — | — |
'Logistic' | Logistic Distribution | μ mean | σ scale parameter | — | — |
'LogLogistic' | Loglogistic Distribution | μ mean of logarithmic values | σ scale parameter of logarithmic values | — | — |
'LogNormal' | Lognormal Distribution | μ mean of logarithmic values | σ standard deviation of logarithmic values | — | — |
'Pearson' | Pearson Distribution | μ mean | σ standard deviation | γ skewness | κ kurtosis |
'Nakagami' | Nakagami Distribution | μ shape parameter | ω scale parameter | — | — |
'Negative Binomial' or
'nbin' | Negative Binomial Distribution | r number of successes | p probability of success in a single trial | — | — |
'Noncentral F' or
'ncf' | Noncentral F Distribution | ν1 numerator degrees of freedom | ν2 denominator degrees of freedom | δ noncentrality parameter | — |
'Noncentral t' or
'nct' | Noncentral t Distribution | ν degrees of freedom | δ noncentrality parameter | — | — |
'Noncentral Chi-square' or
'ncx2' | Noncentral Chi-Square Distribution | ν degrees of freedom | δ noncentrality parameter | — | — |
'Normal' | Normal Distribution | μ mean | σ standard deviation | — | — |
'Poisson' | Poisson Distribution | λ mean | — | — | — |
'Rayleigh' | Rayleigh Distribution | b scale parameter | — | — | — |
'Rician' | Rician Distribution | s noncentrality parameter | σ scale parameter | — | — |
'Stable' | Stable Distribution | α first shape parameter | β second shape parameter | γ scale parameter | δ location parameter |
'T' | Student's t Distribution | ν degrees of freedom | — | — | — |
'tLocationScale' | t Location-Scale Distribution | μ location parameter | σ scale parameter | ν 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 Distribution | a scale parameter | b shape parameter | — | — |
Example: 'Normal'
A
— First probability distribution parameter
scalar value | array of scalar values
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
B
— Second probability distribution parameter
scalar value | array of scalar values
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
C
— Third probability distribution parameter
scalar value | array of scalar values
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
D
— Fourth probability distribution parameter
scalar value | array of scalar values
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
pd
— Probability distribution
probability distribution object
Probability distribution, specified as one of the probability distribution objects in this table.
Distribution Object | Function or App to Create Probability Distribution Object |
---|---|
BetaDistribution | makedist , fitdist , Distribution Fitter |
BinomialDistribution | makedist , fitdist ,
Distribution Fitter |
BirnbaumSaundersDistribution | makedist , fitdist ,
Distribution Fitter |
BurrDistribution | makedist , fitdist ,
Distribution Fitter |
ExponentialDistribution | makedist , fitdist ,
Distribution Fitter |
ExtremeValueDistribution | makedist , fitdist ,
Distribution Fitter |
GammaDistribution | makedist , fitdist ,
Distribution Fitter |
GeneralizedExtremeValueDistribution | makedist , fitdist ,
Distribution Fitter |
GeneralizedParetoDistribution | makedist , fitdist ,
Distribution Fitter |
HalfNormalDistribution | makedist , fitdist ,
Distribution Fitter |
InverseGaussianDistribution | makedist , fitdist ,
Distribution Fitter |
KernelDistribution | fitdist , Distribution Fitter |
LogisticDistribution | makedist , fitdist ,
Distribution Fitter |
LoglogisticDistribution | makedist , fitdist ,
Distribution Fitter |
LognormalDistribution | makedist , fitdist ,
Distribution Fitter |
LoguniformDistribution | makedist |
MultinomialDistribution | makedist |
NakagamiDistribution | makedist , fitdist ,
Distribution Fitter |
NegativeBinomialDistribution | makedist , fitdist ,
Distribution Fitter |
NormalDistribution | makedist , fitdist ,
Distribution Fitter |
Piecewise distribution with generalized Pareto distributions in the tails | paretotails |
PiecewiseLinearDistribution | makedist |
PoissonDistribution | makedist , fitdist ,
Distribution Fitter |
RayleighDistribution | makedist , fitdist ,
Distribution Fitter |
RicianDistribution | makedist , fitdist ,
Distribution Fitter |
StableDistribution | makedist , fitdist ,
Distribution Fitter |
tLocationScaleDistribution | makedist , fitdist ,
Distribution Fitter |
TriangularDistribution | makedist |
UniformDistribution | makedist |
WeibullDistribution | makedist , fitdist ,
Distribution Fitter |
sz1,...,szN
— Size of each dimension (as separate arguments)
integer values
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
, thenR
is a square matrix of sizesz1
-by-sz1
.If the size of any dimension is
0
or negative, thenR
is an empty array.Beyond the second dimension,
random
ignores trailing dimensions with a size of 1. For example, specifying3,1,1,1
produces a 3-by-1 vector of random numbers.
Example: 5,3,2
Data Types: single
| double
sz
— Size of each dimension (as a row vector)
row vector of integers
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]
, thenR
is a square matrix of sizesz1
-by-sz1
.If the size of any dimension is
0
or negative, thenR
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
R
— Random number
scalar value | array of scalar values
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 namename
or a probability distribution objectpd
. It is faster to use a distribution-specific function, such asrandn
andnormrnd
for the normal distribution andbinornd
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.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
The input argument
name
must be a compile-time constant. For example, to use the normal distribution, includecoder.Constant('Normal')
in the-args
value ofcodegen
(MATLAB Coder).Code generation does not support the probability distribution object (
pd
) input argument.
For more information on code generation, see Introduction to Code Generation and General Code Generation Workflow.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced before R2006aR2023b: Support for Pearson distributions
Starting in R2023b, random
supports Pearson distributions.
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