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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)

DistributionDistribution ObjectApps and Interactive UIsDistribution-Specific FunctionsGeneric Functions
BetaBetaDistributionDistribution Fitter
Probability Distribution Function
randtool
betapdf
betacdf
betainv
betastat
betafit
betalike
betarnd
pdf
cdf
icdf
random
mle
Birnbaum-SaundersBirnbaumSaundersDistributionDistribution Fitterpdf
cdf
icdf
random
mle
Burr Type XII BurrDistributionDistribution Fitter
Probability Distribution Function
randtool
pdf
cdf
icdf
random
mle
ExponentialExponentialDistributionDistribution Fitter
Probability Distribution Function
randtool
exppdf
expcdf
expinv
expstat
expfit
explike
exprnd
pdf
cdf
icdf
random
mle
Extreme valueExtremeValueDistributionDistribution Fitter
Probability Distribution Function
randtool
evpdf
evcdf
evinv
evstat
evfit
evlike
evrnd
pdf
cdf
icdf
random
mle
GammaGammaDistributionDistribution Fitter
Probability Distribution Function
randtool
gampdf
gamcdf
gaminv
gamstat
gamfit
gamlike
gamrnd
randg
pdf
cdf
icdf
random
mle
Generalized extreme valueGeneralizedExtremeValueDistributionDistribution Fitter
Probability Distribution Function
randtool
gevpdf
gevcdf
gevinv
gevstat
gevfit
gevlike
gevrnd
pdf
cdf
icdf
random
mle
Generalized ParetoGeneralizedParetoDistributionDistribution Fitter
Probability Distribution Function
randtool
gppdf
gpcdf
gpinv
gpstat
gpfit
gplike
gprnd
pdf
cdf
icdf
random
mle
Half-NormalHalfNormalDistributionDistribution Fitter
Probability Distribution Function
randtool
pdf
cdf
icdf
random
mle
Inverse GaussianInverseGaussianDistributionDistribution Fitterpdf
cdf
icdf
random
mle
LogisticLogisticDistributionDistribution Fitterpdf
cdf
icdf
random
mle
LoglogisticLoglogisticDistributionDistribution Fitterpdf
cdf
icdf
random
mle
LognormalLognormalDistributionDistribution Fitter
Probability Distribution Function
randtool
lognpdf
logncdf
logninv
lognstat
lognfit
lognlike
lognrnd
pdf
cdf
icdf
random
mle
LoguniformLoguniformDistributionpdf
cdf
icdf
random
NakagamiNakagamiDistributionDistribution Fitterpdf
cdf
icdf
random
mle
Normal (Gaussian)NormalDistributionDistribution Fitter
Probability Distribution Function
randtool
normpdf
normcdf
norminv
normstat
normfit
normlike
normrnd
pdf
cdf
icdf
random
mle
Piecewise linearPiecewiseLinearDistribution
RayleighRayleighDistributionDistribution Fitter
Probability Distribution Function
randtool
raylpdf
raylcdf
raylinv
raylstat
raylfit
raylrnd
pdf
cdf
icdf
random
mle
RicianRicianDistributionDistribution Fitterpdf
cdf
icdf
random
mle
StableStableDistributionDistribution Fitter
pdf
cdf
icdf
random
mle
TriangularTriangularDistribution
Uniform (continuous)UniformDistributionProbability Distribution Function
randtool
unifpdf
unifcdf
unifinv
unifstat
unifit
unifrnd
pdf
cdf
icdf
random
mle
WeibullWeibullDistributionDistribution Fitter
Probability Distribution Function
randtool
wblpdf
wblcdf
wblinv
wblstat
wblfit
wbllike
wblrnd
pdf
cdf
icdf
random
mle

Continuous Distributions (Statistics)

Discrete Distributions

Multivariate Distributions

DistributionDistribution ObjectDistribution-Specific Functions
Copula (Gaussian copula, t copula, Clayton copula, Frank copula, Gumbel copula)copulapdf
copulacdf
copulaparam
copulastat
copulafit
copularnd
Gaussian Mixturegmdistributionfitgmdist
pdf
cdf
random
Inverse Wishartiwishrnd
Multivariate normalmvnpdf
mvncdf
mvnrnd
Multivariate tmvtpdf
mvtcdf
mvtrnd
Wishartwishrnd

Nonparametric Distributions

DistributionDistribution ObjectsApps and Interactive UIsDistribution-Specific Functions
KernelKernelDistributionDistribution Fitterksdensity
Pareto tailsparetotails

Flexible Distribution Families

DistributionDistribution-Specific FunctionsGeneric Functions
Pearson systempearspdf
pearscdf
pearsrnd
pdf
cdf
random
Johnson systemjohnsrnd

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