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

Fit probability distributions to data

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

`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 (Since R2022b)
`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

`Probability Distribution Function Tool`	Interactive density and distribution plots
`plot`	Plot probability distribution object (Since R2022b)
`qqplot`	Quantile-quantile plot
`randtool`	Interactive random number generation

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.