Supported Distributions

Statistics and Machine Learning Toolbox™ supports various probability distributions, including parametric, nonparametric, continuous, and discrete distributions. The following tables list the supported probability distributions and supported ways to work with each distribution. For more information, see Working with Probability Distributions.

For a custom probability distribution, use a custom distribution template to create a probability object and then use the Distribution Fitter app or probability object functions. For details, see Define Custom Distributions Using the Distribution Fitter App. You can also define a custom distribution using a function handle and use the mle function to find maximum likelihood estimates. For an example, see Fit Custom Distributions.

Continuous Distributions (Data)

Distribution	Distribution Object	Apps and Interactive UIs	Distribution-Specific Functions	Generic Functions
Beta	`BetaDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`betapdf` `betacdf` `betainv` `betastat` `betafit` `betalike` `betarnd`	`pdf` `cdf` `icdf` `random` `mle`
Birnbaum-Saunders	`BirnbaumSaundersDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Burr Type XII	`BurrDistribution`	Distribution Fitter Probability Distribution Function `randtool`	—	`pdf` `cdf` `icdf` `random` `mle`
Exponential	`ExponentialDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`exppdf` `expcdf` `expinv` `expstat` `expfit` `explike` `exprnd`	`pdf` `cdf` `icdf` `random` `mle`
Extreme value	`ExtremeValueDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`evpdf` `evcdf` `evinv` `evstat` `evfit` `evlike` `evrnd`	`pdf` `cdf` `icdf` `random` `mle`
Gamma	`GammaDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`gampdf` `gamcdf` `gaminv` `gamstat` `gamfit` `gamlike` `gamrnd` `randg`	`pdf` `cdf` `icdf` `random` `mle`
Generalized extreme value	`GeneralizedExtremeValueDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`gevpdf` `gevcdf` `gevinv` `gevstat` `gevfit` `gevlike` `gevrnd`	`pdf` `cdf` `icdf` `random` `mle`
Generalized Pareto	`GeneralizedParetoDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`gppdf` `gpcdf` `gpinv` `gpstat` `gpfit` `gplike` `gprnd`	`pdf` `cdf` `icdf` `random` `mle`
Half-Normal	`HalfNormalDistribution`	Distribution Fitter Probability Distribution Function `randtool`	—	`pdf` `cdf` `icdf` `random` `mle`
Inverse Gaussian	`InverseGaussianDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Logistic	`LogisticDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Loglogistic	`LoglogisticDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Lognormal	`LognormalDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`lognpdf` `logncdf` `logninv` `lognstat` `lognfit` `lognlike` `lognrnd`	`pdf` `cdf` `icdf` `random` `mle`
Loguniform	`LoguniformDistribution`	—	—	`pdf` `cdf` `icdf` `random`
Nakagami	`NakagamiDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Normal (Gaussian)	`NormalDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`normpdf` `normcdf` `norminv` `normstat` `normfit` `normlike` `normrnd`	`pdf` `cdf` `icdf` `random` `mle`
Piecewise linear	`PiecewiseLinearDistribution`	—	—	—
Rayleigh	`RayleighDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`raylpdf` `raylcdf` `raylinv` `raylstat` `raylfit` `raylrnd`	`pdf` `cdf` `icdf` `random` `mle`
Rician	`RicianDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Stable	`StableDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`
Triangular	`TriangularDistribution`	—	—	—
Uniform (continuous)	`UniformDistribution`	Probability Distribution Function `randtool`	`unifpdf` `unifcdf` `unifinv` `unifstat` `unifit` `unifrnd`	`pdf` `cdf` `icdf` `random` `mle`
Weibull	`WeibullDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`wblpdf` `wblcdf` `wblinv` `wblstat` `wblfit` `wbllike` `wblrnd`	`pdf` `cdf` `icdf` `random` `mle`

Continuous Distributions (Statistics)

Distribution	Distribution Object	Apps and Interactive UIs	Distribution-Specific Functions	Generic Functions
Chi-square	—	Probability Distribution Function `randtool`	`chi2pdf` `chi2cdf` `chi2inv` `chi2stat` `chi2rnd`	`pdf` `cdf` `icdf` `random`
F	—	Probability Distribution Function `randtool`	`fpdf` `fcdf` `finv` `fstat` `frnd`	`pdf` `cdf` `icdf` `random`
Noncentral chi-square	—	Probability Distribution Function `randtool`	`ncx2pdf` `ncx2cdf` `ncx2inv` `ncx2stat` `ncx2rnd`	`pdf` `cdf` `icdf` `random`
Noncentral F	—	Probability Distribution Function `randtool`	`ncfpdf` `ncfcdf` `ncfinv` `ncfstat` `ncfrnd`	`pdf` `cdf` `icdf` `random`
Noncentral t	—	Probability Distribution Function `randtool`	`nctpdf` `nctcdf` `nctinv` `nctstat` `nctrnd`	`pdf` `cdf` `icdf` `random`
Student's t	—	Probability Distribution Function `randtool`	`tpdf` `tcdf` `tinv` `tstat` `trnd`	`pdf` `cdf` `icdf` `random`
t location-scale	`tLocationScaleDistribution`	Distribution Fitter	—	`pdf` `cdf` `icdf` `random` `mle`

Discrete Distributions

Distribution	Distribution Objects	Apps and Interactive UIs	Distribution-Specific Functions	Generic Functions
Binomial	`BinomialDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`binopdf` `binocdf` `binoinv` `binostat` `binofit` `binornd`	`pdf` `cdf` `icdf` `random` `mle`
Bernoulli	—	—	—	`mle`
Geometric	—	Probability Distribution Function `randtool`	`geopdf` `geocdf` `geoinv` `geostat` `mle` `geornd`	`pdf` `cdf` `icdf` `random` `mle`
Hypergeometric	—	Probability Distribution Function `randtool`	`hygepdf` `hygecdf` `hygeinv` `hygestat` `hygernd`	`pdf` `cdf` `icdf` `random` `mle`
Multinomial	`MultinomialDistribution`	—	`mnpdf` `mnrnd`	—
Negative binomial	`NegativeBinomialDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`nbinpdf` `nbincdf` `nbininv` `nbinstat` `nbinfit` `nbinrnd`	`pdf` `cdf` `icdf` `random` `mle`
Poisson	`PoissonDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`poisspdf` `poisscdf` `poissinv` `poisstat` `poissfit` `poissrnd`	`pdf` `cdf` `icdf` `random` `mle`
Uniform (discrete)	—	Probability Distribution Function `randtool`	`unidpdf` `unidcdf` `unidinv` `unidstat` `unidrnd`	`pdf` `cdf` `icdf` `random` `mle`

Multivariate Distributions

Distribution	Distribution Object	Distribution-Specific Functions
Copula (Gaussian copula, t copula, Clayton copula, Frank copula, Gumbel copula)	—	`copulapdf` `copulacdf` `copulaparam` `copulastat` `copulafit` `copularnd`
Gaussian Mixture	`gmdistribution`	`fitgmdist` `pdf` `cdf` `random`
Inverse Wishart	—	`iwishrnd`
Multivariate normal	—	`mvnpdf` `mvncdf` `mvnrnd`
Multivariate t	—	`mvtpdf` `mvtcdf` `mvtrnd`
Wishart	—	`wishrnd`

Nonparametric Distributions

Distribution	Distribution Objects	Apps and Interactive UIs	Distribution-Specific Functions
Kernel	`KernelDistribution`	Distribution Fitter	`ksdensity`
Pareto tails	`paretotails`	—	—
Empirical	`EmpiricalDistribution`	—	`ecdf`

Flexible Distribution Families

Distribution	Distribution Objects	Distribution-Specific Functions	Generic Functions
Pearson system	`PearsonDistribution`	`pearspdf` `pearscdf` `pearsrnd` `pearsinv`	`pdf` `cdf` `random` `icdf`
Johnson system	—	`johnsrnd`	—