# PoissonDistribution

Poisson probability distribution object

## Description

A `PoissonDistribution` object consists of parameters, a model description, and sample data for a Poisson probability 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, etc. If the number of counts follows the Poisson distribution, then the interval between individual counts follows the exponential distribution.

The Poisson distribution uses the following parameters.

ParameterDescriptionSupport
`lambda`Mean$\lambda \ge 0$

## Creation

There are several ways to create a `PoissonDistribution` probability distribution object.

## Properties

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### Distribution Parameter

Mean of the Poisson distribution, stored as a nonnegative scalar value.

Data Types: `single` | `double`

### Distribution Characteristics

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. If `IsTruncated` equals `0`, the distribution is not truncated. If `IsTruncated` equals `1`, the distribution is truncated.

Data Types: `logical`

This property is read-only.

Number of parameters for the probability distribution, specified as a positive integer value.

Data Types: `double`

This property is read-only.

Covariance matrix of the parameter estimates, specified as a p-by-p matrix, where p is the number of parameters in the distribution. The (`i`,`j`) element is the covariance between the estimates of the `i`th parameter and the `j`th parameter. The (`i`,`i`) element is the estimated variance of the `i`th parameter. If parameter `i` is fixed rather than estimated by fitting the distribution to data, then the (`i`,`i`) elements of the covariance matrix are 0.

Data Types: `double`

This property is read-only.

Logical flag for fixed parameters, specified as an array of logical values. If `0`, the corresponding parameter in the `ParameterNames` array is not fixed. If `1`, the corresponding parameter in the `ParameterNames` array is fixed.

Data Types: `logical`

This property is read-only.

Distribution parameter values, specified as a vector of scalar values.

Data Types: `single` | `double`

This property is read-only.

Truncation interval for the probability distribution, specified as a vector of scalar values containing the lower and upper truncation boundaries.

Data Types: `single` | `double`

### Other Object Properties

This property is read-only.

Probability distribution name, specified as a character vector.

Data Types: `char`

This property is read-only.

Data used for distribution fitting, specified as a structure containing the following:

• `data`: Data vector used for distribution fitting.

• `cens`: Censoring vector, or empty if none.

• `freq`: Frequency vector, or empty if none.

Data Types: `struct`

This property is read-only.

Distribution parameter descriptions, specified as a cell array of character vectors. Each cell contains a short description of one distribution parameter.

Data Types: `char`

This property is read-only.

Distribution parameter names, specified as a cell array of character vectors.

Data Types: `char`

## Object Functions

 `cdf` Cumulative distribution function `gather` Gather properties of Statistics and Machine Learning Toolbox object from GPU `icdf` Inverse cumulative distribution function `iqr` Interquartile range of probability distribution `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 `plot` Plot probability distribution object `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

## Examples

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Create a Poisson distribution object using the default parameter values.

`pd = makedist('Poisson')`
```pd = PoissonDistribution Poisson distribution lambda = 1 ```

Create a Poisson distribution object by specifying the parameter values.

`pd = makedist('Poisson','lambda',5)`
```pd = PoissonDistribution Poisson distribution lambda = 5 ```

Compute the variance of the distribution.

`v = var(pd)`
```v = 5 ```

For the Poisson distribution, both the mean and variance are equal to the parameter lambda.

## Version History

Introduced in R2013a