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# Documentation

## Working with Probability Distributions

### Types of Probability Distributions

Probability distributions are theoretical distributions based on assumptions about a source population. The distributions assign probability to the event that a random variable has a specific, discrete value, or falls within a specified range of continuous values. The two main types of distributions are parametric and nonparametric.

Parametric distributions are probability distributions that you can describe using a finite set of parameters. You can choose a distribution model for your data based on a parametric family of probability distributions, and then adjust the parameters to fit the data. You can then perform further analyses by computing summary statistics, evaluating the probability density function (pdf) and cumulative distribution function (cdf), and assessing the fit of the distribution to your data.

Nonparametric and empirical distributions provide estimates of probability density functions (pdf) or cumulative distribution functions (cdf) based on sample data. You can use this approach when the data cannot be described accurately by the supported parametric distributions. Statistics Toolbox™ supports the following nonparametric and empirical techniques:

• Kernel distribution

• Piecewise linear distribution

• Empirical cumulative distribution function

• Piecewise distribution with Pareto tails

• Triangular distribution

### How to Work with Probability Distributions

Statistics Toolbox provides several ways to work with parametric and nonparametric probability distributions.

Apps and user interfaces provide an interactive approach to working with parametric and nonparametric probability distributions.

• Use the Distribution Fitting app to fit a distribution to your data and export a probability distribution object to your workspace for further analysis.

• Use the Probability Distribution Function user interface to visually explore probability distributions.

• Use the Random Number Generation user interface to generate random data from a specified distribution and export the results to your workspace.

Probability distribution objects provide a convenient way to explore and fit your data to a parametric or nonparametric distribution, save the results to a single entity, and generate random data from the resulting parameters.

Command-line functions let you further explore parametric and nonparametric distributions, fit relevant models to your data, and generate random data. You can use command-line functions to work with distributions that are not currently supported as probability distribution objects.