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 ∞.
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.