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Multivariate Statistics Package Symbol

MultiPoissonDistribution

MultiPoissonDistribution[

₀,

]
represents a multivariate Poisson distribution with mean vector

₀+

To use MultiPoissonDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].

The multivariate Poisson distribution MultiPoissonDistribution[₀, ] with ={₁, ₂, ...} is the distribution followed by a Poisson with mean ₀ summed with a vector of independent Poissons with means ₁, ₂,....

MultiPoissonDistribution can be used with such functions as Mean, PDF and RandomInteger.

The mean of a multivariate Poisson distribution:

The variances of each dimension:

Probability density function:

Needs["MultivariateStatistics`"]

The mean of a multivariate Poisson distribution:

Needs["MultivariateStatistics`"]

The variances of each dimension:

Needs["MultivariateStatistics`"]

Probability density function:

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

MultiPoissonDistribution is not defined when

₀ is not positive:

MultiPoissonDistribution is not defined when any of the elements of

are not positive:

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