# Documentation

## 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 (dfittool), to interactively fit a distribution to sample data, and export a probability distribution object to the workspace.

• The Probability Distribution Function user interface (disttool), 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

DistributionUsing ObjectsLegacy FunctionsApps/UIs
Nonparametric (kernel)KernelDistributionksdensitydfittool
Paretoparetotails

### Flexible Distribution Families

DistributionUsing ObjectsLegacy FunctionsApps/UIs
Pearson system pearsrnd
Johnson system johnsrnd