Supported Distributions

统计和机器学习工具箱™ 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, seeWorking 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, seeDefine Custom Distributions Using the Distribution Fitter App. You can also define a custom distribution using a function handle and use themlefunction to find maximum likelihood estimates. For an example, seeFit Custom Distributions.

连续分布（数据）

Distribution	Distribution Object	Apps and Interactive UIs	Distribution-Specific Functions	Generic Functions
Beta	`BetaDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`betapdf` `betacdf` `betainv` `betastat` `贝菲特` `betalike` `betarnd`	`pdf` `cdf` `ICDF` `random` `mle`
Birnbaum-Saunders	`BirnbaumSaundersDistribution`	Distribution Fitter	—	`pdf` `cdf` `ICDF` `random` `mle`
Burr Type XII	`伯德分布`	Distribution Fitter Probability Distribution Function `randtool`	—	`pdf` `cdf` `ICDF` `random` `mle`
Exponential	`ExponentialDistribution`	Distribution Fitter Probability Distribution Function `randtool`	`exppdf` `expcdf` `探索` `expstat` `解释` `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`
伽玛	`伽马分布`	Distribution Fitter Probability Distribution Function `randtool`	`gampdf` `gamcdf` `gaminv` `gamstat` `gamfit` `gamlike` `gamrnd` `randg`	`pdf` `cdf` `ICDF` `random` `mle`
普遍的极值	`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`
半正常	`半normaldistribution`	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`
logisriform	`logisriformDistribution`	—	—	`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	`分段分布`	—	—	—
Rayleigh	`雷利德分布`	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`
稳定的	`稳定的Distribution`	Distribution Fitter	—	`pdf` `cdf` `ICDF` `random` `mle`
三角形	`三角分裂`	—	—	—
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`

连续分布（统计）

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`
NoncentralF	—	Probability Distribution Function `randtool`	`NCFPDF` `ncfcdf` `ncfinv` `ncfstat` `ncfrnd`	`pdf` `cdf` `ICDF` `random`
Noncentralt	—	Probability Distribution Function `randtool`	`nctpdf` `NCTCDF` `nctinv` `nctstat` `nctrnd`	`pdf` `cdf` `ICDF` `random`
Student'st	—	Probability Distribution Function `randtool`	`TPDF` `tcdf` `tinv` `tstat` `trnd`	`pdf` `cdf` `ICDF` `random`
t位置尺度	`tLocationScaleDistribution`	Distribution Fitter	—	`pdf` `cdf` `ICDF` `random` `mle`

Discrete Distributions

Distribution	Distribution Objects	Apps and Interactive UIs	Distribution-Specific Functions	Generic Functions
二项式	`二项分布`	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`
多项式	`多项式Distribution`	—	`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`
统一（离散）	—	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,tCopula，Clayton Copula，Frank Copula，Gumbel Copula）	—	`copulapdf` `copulacdf` `copulaparam` `copulastat` `copulafit` `copularnd`
Gaussian Mixture	`gmdistribution`	`fitgmdist` `pdf` `cdf` `random`
倒数的怀疑	—	`iwishrnd`
Multivariate normal	—	`mvnpdf` `mvncdf` `mvnrnd`
Multivariatet	—	`mvtpdf` `mvtcdf` `mvtrnd`
Wishart	—	`愿望`

非参数分布

Distribution	Distribution Objects	Apps and Interactive UIs	Distribution-Specific Functions
Kernel	`kerneldistribution`	Distribution Fitter	`ksdensity`
Pareto tails	`paretotails`	—	—

Flexible Distribution Families

Distribution	Distribution-Specific Functions
Pearson system	`梨子`
约翰逊系统	`johnsrnd`