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Supported Distributions

Probability distributions supported by the Statistics Toolbox™ are cross-referenced with their supporting functions and GUIs in the following tables. The tables use the following abbreviations for distribution functions:

For more detailed explanations of each supported distribution, see Distribution Reference.

Parametric Distributions

Continuous Distributions (Data)

Namepdfcdfinvstatfitlikernd

Beta

betapdf, pdfbetacdf, cdfbetainv, icdfbetastatbetafit, fitdist, mle, dfittoolbetalikebetarnd, random, randtool

Birnbaum- Saunders

pdfcdficdf mle, fitdist, dfittool random

Burr Type XII

pdfcdficdf mle, fitdist, dfittool random, randtool

Exponential

exppdf, pdfexpcdf, cdfexpinv, icdfexpstatexpfit, mle, fitdist, dfittoolexplikeexprnd, random, randtool

Extreme value

evpdf, pdfevcdf, cdfevinv, icdfevstatevfit, mle, fitdist, dfittoolevlikeevrnd, random, randtool

Gamma

gampdf, pdfgamcdf, cdfgaminv, icdfgamstatgamfit, mle, fitdist, dfittoolgamlikegamrnd, randg, random, randtool

Generalized extreme value

gevpdf, pdfgevcdf, cdfgevinv, icdfgevstatgevfit, mle, fitdist, dfittoolgevlikegevrnd, random, randtool

Generalized Pareto

gppdf, pdfgpcdf, cdfgpinv, icdfgpstatgpfit, mle, fitdist, dfittoolgplikegprnd, random, randtool

Inverse Gaussian

pdfcdficdf mle, fitdist, dfittool random

Johnson system

    johnsrnd johnsrnd

Logistic

pdfcdficdf mle, fitdist, dfittool random

Loglogistic

pdfcdficdf mle, fitdist, dfittool random

Lognormal

lognpdf, pdflogncdf, cdflogninv, icdflognstatlognfit, mle, fitdist, dfittoollognlikelognrnd, random, randtool

Nakagami

pdfcdficdf mle, fitdist, dfittool random

Normal (Gaussian)

normpdf, pdfnormcdf, cdfnorminv, icdfnormstatnormfit, mle, fitdist, dfittoolnormlikenormrnd, randn, random, randtool

Pearson system

    pearsrnd pearsrnd

Piecewise

pdfcdficdf paretotails random

Rayleigh

raylpdf, pdfraylcdf, cdfraylinv, icdfraylstatraylfit, mle, fitdist, dfittool raylrnd, random, randtool

Rician

pdfcdficdf mle, fitdist, dfittool random

Uniform (continuous)

unifpdf, pdfunifcdf, cdfunifinv, icdfunifstatunifit, mle unifrnd, rand, random

Weibull

wblpdf, pdfwblcdf, cdfwblinv, icdfwblstatwblfit, mle, fitdist, dfittoolwbllikewblrnd, random

Continuous Distributions (Statistics)

Namepdfcdfinvstatfitlikernd

Chi-square

chi2pdf, pdfchi2cdf, cdfchi2inv, icdfchi2stat  chi2rnd, random, randtool

F

fpdf, pdffcdf, cdffinv, icdffstat  frnd, random, randtool

Noncentral chi-square

ncx2pdf, pdfncx2cdf, cdfncx2inv, icdfncx2stat  ncx2rnd, random, randtool

Noncentral F

ncfpdf, pdfncfcdf, cdfncfinv, icdfncfstat  ncfrnd, random, randtool

Noncentral t

nctpdf, pdfnctcdf, cdfnctinv, icdfnctstat  nctrnd, random, randtool

Student's t

tpdf, pdftcdf, cdftinv, icdftstat  trnd, random, randtool

t location- scale

pdfcdficdf mle, fitdist, dfittool random

Discrete Distributions

Namepdfcdfinvstatfitlikernd

Binomial

binopdf, pdfbinocdf, cdfbinoinv, icdfbinostatbinofit, mle, fitdist, dfittool binornd, random, randtool

Bernoulli

    mle  

Geometric

geopdf, pdfgeocdf, cdfgeoinv, icdfgeostatmle geornd, random, randtool

Hypergeometric

hygepdf, pdfhygecdf, cdfhygeinv, icdfhygestat  hygernd, random

Multinomial

mnpdf     mnrnd

Negative binomial

nbinpdf, pdfnbincdf, cdfnbininv, icdfnbinstatnbinfit, mle, fitdist, dfittool nbinrnd, random, randtool

Poisson

poisspdf, pdfpoisscdf, cdfpoissinv, icdfpoisstatpoissfit, mle, fitdist, dfittool poissrnd, random, randtool

Uniform (discrete)

unidpdf, pdfunidcdf, cdfunidinv, icdfunidstatmle unidrnd, random, randtool

Multivariate Distributions

Namepdfcdfinvstatfitlikernd

Gaussian copula

copulapdfcopulacdf copulastatcopulafit copularnd

Gaussian mixture

pdfcdf  fit random

t copula

copulapdfcopulacdf copulastatcopulafit copularnd

Clayton copula

copulapdfcopulacdf copulastatcopulafit copularnd

Frank copula

copulapdfcopulacdf copulastatcopulafit copularnd

Gumbel copula

copulapdfcopulacdf copulastatcopulafit copularnd

Inverse Wishart

      iwishrnd

Multivariate normal

mvnpdfmvncdf    mvnrnd

Multivariate t

mvtpdfmvtcdf    mvtrnd

Wishart

      wishrnd

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