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Supported Distributions

Statistics and Machine Learning Toolbox™ supports more than 30 probability distributions, including parametric, nonparametric, continuous, and discrete distributions.

The toolbox provides several ways to work with probability distributions.

  • Use probability distribution objects to fit a probability distribution object to sample data, or to create a probability distribution object with specified parameter values. Once you create a probability distribution object, you can use object functions to:

    • Compute confidence intervals for the distribution parameters (paramci).

    • Compute summary statistics, including mean (mean), median (median), interquartile range (iqr), variance (var), and standard deviation (std).

    • Evaluate the probability density function (pdf).

    • Evaluate the cumulative distribution function (cdf) or the inverse cumulative distribution function (icdf).

    • Compute the negative loglikelihood (negloglik) and profile likelihood function (proflik) for the distribution.

    • Generate random numbers from the distribution (random).

    • Truncate the distribution to specified lower and upper limits (truncate).

    Each distribution object page provides information about the object’s properties and the functions you can use to work with the object.

  • Use probability distribution functions to work with data input from matrices. Some of the supported distributions have distribution-specific functions. These functions use the following abbreviations, as in normpdf, normcdf, norminv, normstat, normfit, normlike, and normrnd:

    • pdf — Probability density functions

    • cdf — Cumulative distribution functions

    • inv — Inverse cumulative distribution functions

    • stat — Distribution statistics functions

    • fit — Distribution Fitter functions

    • like — Negative loglikelihood functions

    • rnd — Random number generators

    You can also use the following generic functions to work with most of the distributions:

    • pdf — Probability density function

    • cdf — Cumulative distribution function

    • icdf — Inverse cumulative distribution function

    • random — Random number generating function

    • mle — Distribution fitting function

  • Use probability distribution apps and user interfaces to interactively fit, explore, and generate random numbers from probability distributions. Available apps and user interfaces include:

    • The Distribution Fitter app, to interactively fit a distribution to sample data, and export a probability distribution object to the workspace.

    • The Probability Distribution Function user interface, to visually explore the effect on the pdf and cdf of changing the distribution parameter values.

    • The Random Number Generation user interface (randtool), to interactively generate random numbers from a probability distribution with specified parameter values and export them to the workspace.

For more information on the different ways to work with probability distributions, see Working with Probability Distributions.

Continuous Distributions (Data)

DistributionDistribution ObjectsDistribution-Specific FunctionsGeneric FunctionsApps and UIs
BetaBetaDistributionbetapdf
betacdf
betainv
betastat
betafit
betalike
betarnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Birnbaum-SaundersBirnbaumSaundersDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
Burr Type XII BurrDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
ExponentialExponentialDistributionexppdf
expcdf
expinv
expstat
expfit
explike
exprnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Extreme valueExtremeValueDistributionevpdf
evcdf
evinv
evstat
evfit
evlike
evrnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
GammaGammaDistributiongampdf
gamcdf
gaminv
gamstat
gamfit
gamlike
gamrnd
randg
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Generalized extreme valueGeneralizedExtremeValueDistributiongevpdf
gevcdf
gevinv
gevstat
gevfit
gevlike
gevrnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Generalized ParetoGeneralizedParetoDistributiongppdf
gpcdf
gpinv
gpstat
gpfit
gplike
gprnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Half-NormalHalfNormalDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Inverse GaussianInverseGaussianDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
LogisticLogisticDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
LoglogisticLoglogisticDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
LognormalLognormalDistributionlognpdf
logncdf
logninv
lognstat
lognfit
lognlike
lognrnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
NakagamiNakagamiDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
Normal (Gaussian)NormalDistributionnormpdf
normcdf
norminv
normstat
normfit
normlike
normrnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
Piecewise linearPiecewiseLinearDistribution   
RayleighRayleighDistributionraylpdf
raylcdf
raylinv
raylstat
raylfit
raylrnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool
RicianRicianDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
StableStableDistribution pdf
cdf
icdf
random
mle
Distribution Fitter
TriangularTriangularDistribution   
Uniform (continuous)UniformDistributionunifpdf
unifcdf
unifinv
unifstat
unifit
unifrnd
pdf
cdf
icdf
random
mle
Probability Distribution Function
randtool
WeibullWeibullDistributionwblpdf
wblcdf
wblinv
wblstat
wblfit
wbllike
wblrnd
pdf
cdf
icdf
random
mle
Distribution Fitter
Probability Distribution Function
randtool

Continuous Distributions (Statistics)

Discrete Distributions

Multivariate Distributions

DistributionObjectDistribution-Specific FunctionsGeneric FunctionsApps/UI
Copula (Gaussian copula, t copula, Clayton copula, Frank copula, Gumbel copula) copulapdf
copulacdf
copulaparam
copulastat
copulafit
copularnd
  
Gaussian Mixturegmdistributionfitgmdist
pdf
cdf
random
  
Inverse Wishart iwishrnd  
Multivariate normal mvnpdf
mvncdf
mvnrnd
  
Multivariate t mvtpdf
mvtcdf
mvtrnd
  
Wishart wishrnd  

Nonparametric Distributions

DistributionDistribution ObjectsDistribution-Specific FunctionsGeneric FunctionsApps/UIs
KernelKernelDistributionksdensity Distribution Fitter
Pareto tailsparetotails   

Flexible Distribution Families

DistributionDistribution ObjectsDistribution-Specific FunctionsGeneric FunctionsApps/UIs
Pearson system pearsrnd  
Johnson system johnsrnd  

Related Topics