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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. The Using Objects page for each distribution 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, tables, and dataset arrays. Some of the supported distributions have distribution-specific functions. These functions use the following abbreviations:

    • pdf — Probability density functions

    • cdf — Cumulative distribution functions

    • inv — Inverse cumulative distribution functions

    • stat — Distribution statistics functions

    • fit — Distribution fitting functions

    • like — Negative log-likelihood 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

    • mle — Distribution fitting function

    • random — Random number generating 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 Fitting 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)

DistributionUsing ObjectsLegacy FunctionsApps and UIs
BetaBetaDistributionbetapdf
betacdf
betainv
betastat
betafit
betalike
betarnd
Distribution Fitting
Probability Distribution Function
randtool
Birnbaum-SaundersBirnbaumSaundersDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
Burr Type XIIBurrDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
Probability Distribution Function
randtool
ExponentialExponentialDistributionexppdf
expcdf
expinv
expstat
expfit
explike
Distribution Fitting
Probability Distribution Function
randtool
Extreme valueExtremeValueDistributionevpdf
evcdf
evinv
evstat
evfit
evlike
evrnd
Distribution Fitting
Probability Distribution Function
randtool
GammaGammaDistributiongampdf
gamcdf
gaminv
gamstat
gamfit
gamlike
gamrnd
Distribution Fitting
Probability Distribution Function
randtool
Generalized extreme valueGeneralizedExtremeValueDistributiongevpdf
gevcdf
gevinv
gevstat
gevfit
gevlike
gevrnd
Distribution Fitting
Probability Distribution Function
randtool
Generalized ParetoGeneralizedParetoDistributiongppdf
gpcdf
gpinv
gpstat
gpfit
gplike
gprnd
Distribution Fitting
Probability Distribution Function
randtool
Half-Normal DistributionHalfNormalDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
Probability Distribution Function
randtool
Inverse GaussianInverseGaussianDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
LogisticLogisticDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
LoglogisticLoglogisticDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
LognormalLognormalDistributionlognpdf
logncdf
logninv
lognstat
lognfit
lognlike
lognrnd
Distribution Fitting
Probability Distribution Function
randtool
NakagamiNakagamiDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
Normal (Gaussian)NormalDistributionnormpdf
normcdf
norminv
normstat
normfit
normlike
normrnd
Distribution Fitting
Probability Distribution Function
randtool
Piecewise linearPiecewiseLinearDistributionpdf
cdf
icdf
random
 
RayleighRayleighDistributionraylpdf
raylcdf
raylinv
raylstat
raylfit
raylrnd
Distribution Fitting
Probability Distribution Function
randtool
RicianRicianDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
StableStableDistributionpdf
cdf
icdf
mle
random
Distribution Fitting
Probability Distribution Function
randtool
TriangularTriangularDistribution  
Uniform (continuous)UniformDistributionunifpdf
unifcdf
unifinv
unifstat
unifit
unifrnd
Probability Distribution Function
randtool
WeibullWeibullDistributionwblpdf
wblcdf
wblinv
wblstat
wblfit
wbllike
wblrnd
Distribution Fitting
Probability Distribution Function
randtool

Nonparametric Distributions

DistributionUsing ObjectsLegacy FunctionsApps/UIs
Nonparametric (kernel)KernelDistributionksdensityDistribution Fitting
Paretoparetotails  

Flexible Distribution Families

DistributionUsing ObjectsLegacy FunctionsApps/UIs
Pearson system pearsrnd 
Johnson system johnsrnd 

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