Evaluates the Poisson distribution function.

k—Parameter for which the Poisson distribution function is to be evaluated.

theta—Mean of the Poisson distribution. Parameter theta must be positive.

result—The probability that a Poisson random variable takes a value less than or equal to k.

Double—If present and nonzero, double precision is used.

Function POISSONCDF evaluates the distribution function of a Poisson random variable with parameter theta. The mean of the Poisson random variable, theta, must be positive.

The probability function (with θ = theta) is as follows:

The individual terms are calculated from the tails of the distribution to the mode of the distribution and summed. The POISSONCDF function uses the recursive relationship:

Suppose X is a Poisson random variable with θ = 10. This example evaluates the probability that X ≤ 7.

p = POISSONCDF(7, 10)

PM, 'Pr(x <= 7) = ', p, Format = '(a13,f7.4)'

; PV-WAVE prints: Pr(x <= 7) =  0.2202

STAT_LESS_THAN_ZERO— Input parameter, k, is less than zero.