poissonDistribution

The Poisson distribution, its complement, and inverse

k is the number of events. m is the mean. The Poisson distribution is defined as the sum of the first k terms of the Poisson density function. The complement returns the sum of the terms k+1 to ∞.

poissonDistribution = $(BIGSUM j=0, k) e-m mj/j!

poissonDistributionCompl = $(BIGSUM j=k+1, ∞) e-m mj/j!

The terms are not summed directly; instead the incomplete gamma integral is employed, according to the relation

y = poissonDistribution( k, m ) = gammaIncompleteCompl( k+1, m ).

The arguments must both be positive.

real
poissonDistribution
(
int k
,
real m
)

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