# Poisson Distribution

Fit, evaluate, and generate random samples from Poisson distribution

Statistics and Machine Learning Toolbox™ offers several ways to work with the Poisson distribution.

• Create a probability distribution object `PoissonDistribution` by fitting a probability distribution to sample data or by specifying parameter values. Then, use object functions to evaluate the distribution, generate random numbers, and so on.

• Work with the Poisson distribution interactively by using the Distribution Fitter app. You can export an object from the app and use the object functions.

• Use distribution-specific functions with specified distribution parameters. The distribution-specific functions can accept parameters of multiple Poisson distributions.

• Use generic distribution functions (`cdf`, `icdf`, `pdf`, `random`) with a specified distribution name (`'Poisson'`) and parameters.

To learn about the Poisson distribution, see Poisson Distribution.

## Objects

 `PoissonDistribution` Poisson probability distribution object

## Apps

 Distribution Fitter Fit probability distributions to data Probability Distribution Function Interactive density and distribution plots

## Functions

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#### Create `PoissonDistribution` Object

 `makedist` Create probability distribution object `fitdist` Fit probability distribution object to data

#### Work with `PoissonDistribution` Object

 `cdf` Cumulative distribution function `icdf` Inverse cumulative distribution function `iqr` Interquartile range `mean` Mean of probability distribution `median` Median of probability distribution `negloglik` Negative loglikelihood of probability distribution `paramci` Confidence intervals for probability distribution parameters `pdf` Probability density function `proflik` Profile likelihood function for probability distribution `random` Random numbers `std` Standard deviation of probability distribution `truncate` Truncate probability distribution object `var` Variance of probability distribution
 `poisscdf` Poisson cumulative distribution function `poisspdf` Poisson probability density function `poissinv` Poisson inverse cumulative distribution function `poisstat` Poisson mean and variance `poissfit` Poisson parameter estimates `poissrnd` Random numbers from Poisson distribution
 `mle` Maximum likelihood estimates
 `distributionFitter` Open Distribution Fitter app `qqplot` Quantile-quantile plot `randtool` Interactive random number generation

## Topics

Poisson Distribution

The Poisson distribution is appropriate for applications that involve counting the number of times a random event occurs in a given amount of time, distance, area, and so on.