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MultiPoissonDistribution[μ0,μ]

represents a multivariate Poisson distribution with mean vector μ0+μ.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Possible Issues  
See Also
Tech Notes
Related Guides
Cite this Page
MultivariateStatistics`
MultivariateStatistics`

MultiPoissonDistribution

As of Version 8.0, MultiPoissonDistribution has been renamed to MultivariatePoissonDistribution and is part of the built-in Wolfram Language kernel.

MultiPoissonDistribution[μ0,μ]

represents a multivariate Poisson distribution with mean vector μ0+μ.

Details and Options

  • To use MultiPoissonDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
  • The multivariate Poisson distribution MultiPoissonDistribution[μ0,μ] with μ={μ1,μ2,…} is the distribution followed by a Poisson with mean μ0 summed with a vector of independent Poissons with means μ1, μ2, ….
  • The parameter μ0 and the elements of the vector μ can be any positive numbers.
  • MultiPoissonDistribution can be used with such functions as Mean, PDF, and RandomInteger.

Examples

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Basic Examples  (3)

The mean of a multivariate Poisson distribution:

The variances of each dimension:

Probability density function:

Scope  (3)

Generate a set of pseudorandom vectors that follow a multivariate Poisson distribution:

Possible Issues  (2)

MultiPoissonDistribution is not defined when μ0 is not positive:

MultiPoissonDistribution is not defined when any of the elements of μ are not positive:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:

Wolfram Research (2007), MultiPoissonDistribution, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/MultiPoissonDistribution.html.

Text

Wolfram Research (2007), MultiPoissonDistribution, Wolfram Language function, https://reference.wolfram.com/language/MultivariateStatistics/ref/MultiPoissonDistribution.html.

CMS

Wolfram Language. 2007. "MultiPoissonDistribution." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/MultivariateStatistics/ref/MultiPoissonDistribution.html.

APA

Wolfram Language. (2007). MultiPoissonDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/MultivariateStatistics/ref/MultiPoissonDistribution.html

BibTeX

@misc{reference.wolfram_2025_multipoissondistribution, author="Wolfram Research", title="{MultiPoissonDistribution}", year="2007", howpublished="\url{https://reference.wolfram.com/language/MultivariateStatistics/ref/MultiPoissonDistribution.html}", note=[Accessed: 18-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_multipoissondistribution, organization={Wolfram Research}, title={MultiPoissonDistribution}, year={2007}, url={https://reference.wolfram.com/language/MultivariateStatistics/ref/MultiPoissonDistribution.html}, note=[Accessed: 18-August-2025]}