# Documentation

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# random

Random numbers

## Syntax

```Y = random(pd)Y = random(pd,m,n,...)Y = random(pd,[m,n,...])Y = random(name,A)Y = random(name,A,B)Y = random(name,A,B,C)Y = random(name,A,B,C,D)Y = random(name,A,m,n,...)Y = random(name,A,[m,n,...])Y = random(name,A,B,m,n,...)Y = random(name,A,B,[m,n,...])Y = random(name,A,B,C,m,n,...)Y = random(name,A,B,C,[m,n,...])Y = random(name,A,B,C,D,m,n,...)Y = random(name,A,B,C,D,[m,n,...])```

## Description

`Y = random(pd)` returns a random number `Y` from the distribution specified by the probability distribution object `pd`. You can create a probability distribution object with specified parameter values using `makedist`, or fit a probability distribution object to sample data using `fitdist`.

`Y = random(pd,m,n,...)` or ```Y = random(pd,[m,n,...])``` returns an `m`-by-`n`-by... matrix of random numbers from the probability distribution specified by `pd`.

`Y = random(name,A)` where `name` is the name of a distribution that takes a single parameter, returns random numbers `Y` from the one-parameter family of distributions specified by `name`. Parameter values for the distribution are given in `A`.

`Y` is the same size as `A`.

`Y = random(name,A,B)` returns random numbers `Y` from a two-parameter family of distributions. Parameter values for the distribution are given in `A` and `B`.

If `A` and `B` are arrays, they must be the same size. If either `A` or `B` are scalars, they are expanded to constant matrices of the same size.

`Y = random(name,A,B,C)` returns random numbers `Y` from a three-parameter family of distributions. Parameter values for the distribution are given in `A`, `B`, and `C`.

If `A`, `B`, and `C` are arrays, they must be the same size. If any of `A`, `B`, or `C` are scalars, they are expanded to constant matrices of the same size.

`Y = random(name,A,B,C,D)` returns random numbers `Y` from a four-parameter family of distributions. Parameter values for the distribution are given in `A`, `B`, `C`, and `D`.

If `A`, `B`, `C`, and `D` are arrays, they must be the same size. If any of `A`, `B`, `C`, or `D` are scalars, they are expanded to constant matrices of the same size.

`Y = random(name,A,m,n,...)` or ```Y = random(name,A,[m,n,...])``` returns an `m`-by-`n`-by... matrix of random numbers.

Similarly, `Y = random(name,A,B,m,n,...)` or ```Y = random(name,A,B,[m,n,...])``` returns an `m`-by-`n`-by... matrix of random numbers for distributions that require two parameters. ```Y = random(name,A,B,C,m,n,...)``` or `Y = random(name,A,B,C,[m,n,...])` returns an `m`-by-`n`-by... matrix of random numbers for distributions that require three parameters. ```Y = random(name,A,B,C,D,m,n,...)``` or `Y = random(name,A,B,C,D,[m,n,...])` returns an `m`-by-`n`-by... matrix of random numbers for distributions that require four parameters.

If any of `A`, `B`, `C`, or `D` are arrays, then the specified dimensions must match the common dimensions of `A`, `B`, `C`, and `D` after any necessary scalar expansion.

The following table denotes the acceptable values for `name`, as well as the parameters for that distribution:

`name`DistributionInput Parameter AInput Parameter BInput Parameter CInput Parameter D
`'beta'` or `'Beta'`Beta Distribution`a``b`
`'bino'` or `'Binomial'`Binomial Distribution`n`: number of trials`p`: probability of success for each trial
`'birnbaumsaunders'`Birnbaum-Saunders Distributionβγ
`'burr'` or `'Burr'`Burr Type XII Distributionα: scale parameter`c`: shape parameter`k`: shape parameter
`'chi2'` or `'Chisquare'`Chi-Square Distributionν: degrees of freedom
`'exp'` or `'Exponential'`Exponential Distributionμ: mean
`'ev'` or `'Extreme Value'`Extreme Value Distributionμ: location parameterσ: scale parameter
`'f'` or `'F'`F Distributionν`1`: numerator degrees of freedomν`2`: denominator degrees of freedom
`'gam'` or `'Gamma'`Gamma Distribution`a`: shape parameter`b`: scale parameter
`'gev'` or `'Generalized Extreme Value'`Generalized Extreme Value Distribution`k`: shape parameterσ: scale parameterμ: location parameter
`'gp'` or `'Generalized Pareto'`Generalized Pareto Distribution`k`: tail index (shape) parameterσ: scale parameterμ: threshold (location) parameter
`'geo'` or `'Geometric'`Geometric Distribution`p`: probability parameter
`'hn'` or `'Half Normal'`Half-Normal Distributionμ: locationσ: scale
`'hyge'` or `'Hypergeometric'`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 Distributionμλ
`'logistic'`Logistic Distributionμσ
`'loglogistic'`Loglogistic Distributionμσ
`'logn'` or `'Lognormal'`Lognormal Distributionμσ
`'nakagami'`Nakagami Distributionμω
`'nbin'` or `'Negative Binomial'`Negative Binomial Distribution`r`: number of successes`p`: probability of success in a single trial
`'ncf'` or `'Noncentral F'`Noncentral F Distributionν`1`: numerator degrees of freedomν`2`: denominator degrees of freedomδ: noncentrality parameter
`'nct'` or `'Noncentral t'`Noncentral t Distributionν: degrees of freedomδ: noncentrality parameter
`'ncx2'` or `'Noncentral Chi-square'`Noncentral Chi-Square Distributionν: degrees of freedomδ: noncentrality parameter
`'norm'` or `'Normal'`Normal Distributionμ: mean σ: standard deviation
`'poiss'` or `'Poisson'`Poisson Distributionλ: mean
`'rayl'` or `'Rayleigh'`Rayleigh Distribution`b`: scale parameter
`'rician'`Rician Distribution`s`: noncentrality parameterσ: scale parameter
`'stable'`Stable Distributionα: first shape parameterβ: second shape parameterγ: scale parameterδ: location parameter
`'t'` or `'T'`Student's t Distributionν: degrees of freedom
`'tlocationscale'`t Location-Scale Distributionμ: location parameterσ: scale parameterν: shape parameter
`'unif'` or `'Uniform'`Uniform Distribution (Continuous)`a`: lower endpoint (minimum)`b`: upper endpoint (maximum)
`'unid'` or `'Discrete Uniform'`Uniform Distribution (Discrete)`N`: maximum observable value
`'wbl'` or `'Weibull'`Weibull Distribution`a`: scale parameter`b`: shape parameter

## Examples

collapse all

Generate a 2-by-4 array of random values from the normal distribution with mean equal to 0 and standard deviation equal to 1.

```x1 = random('Normal',0,1,2,4) ```
```x1 = 0.5377 -2.2588 0.3188 -0.4336 1.8339 0.8622 -1.3077 0.3426 ```

Generate a single random value from Poisson distributions with rate parameters 1, 2, ..., 6, respectively.

```x2 = random('Poisson',1:6,1,6) ```
```x2 = 4 2 3 7 4 9 ```