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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.


PoissonDistributionPoisson probability distribution object


Distribution FitterFit probability distributions to data
Probability Distribution FunctionInteractive density and distribution plots


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Create PoissonDistribution Object

makedistCreate probability distribution object
fitdistFit probability distribution object to data

Work with PoissonDistribution Object

cdfCumulative distribution function
gatherGather properties of Statistics and Machine Learning Toolbox object from GPU (Since R2020b)
icdfInverse cumulative distribution function
iqrInterquartile range of probability distribution
meanMean of probability distribution
medianMedian of probability distribution
negloglikNegative loglikelihood of probability distribution
paramciConfidence intervals for probability distribution parameters
pdfProbability density function
plotPlot probability distribution object (Since R2022b)
proflikProfile likelihood function for probability distribution
randomRandom numbers
stdStandard deviation of probability distribution
truncateTruncate probability distribution object
varVariance of probability distribution
poisscdfPoisson cumulative distribution function
poisspdfPoisson probability density function
poissinvPoisson inverse cumulative distribution function
poisstatPoisson mean and variance
poissfitPoisson parameter estimates
poissrnd Random numbers from Poisson distribution
mleMaximum likelihood estimates
distributionFitterOpen Distribution Fitter app
plotPlot probability distribution object (Since R2022b)
qqplotQuantile-quantile plot
randtoolInteractive 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.