## 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:

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:

• 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.

### Nonparametric Distributions

DistributionDistribution ObjectsDistribution-Specific FunctionsGeneric FunctionsApps/UIs
Kernel`KernelDistribution``ksdensity` Distribution Fitter
Pareto tails`paretotails`

### Flexible Distribution Families

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