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.

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The mean of a multivariate Poisson distribution:

The variances of each dimension:

Probability density function:

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

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:

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