Evaluates the probability function of a Poisson random variable.

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

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

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

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

POISSONPDF evaluates the probability function of a Poisson random variable with parameter theta. theta, which is the mean of the Poisson random variable, must be positive. The probability function (with θ = theta) is:

POISSONPDF evaluates this function directly, taking logarithms and using the log gamma function.

Suppose X is a Poisson random variable with θ = 10. In this example, we evaluate the probability function at k = 7.

result = POISSONPDF(7, 10.0)

PRINT, "The probability that X is equal to 7 is:"

PRINT, result, Format='(F9.7)'

; PV-WAVE prints the following:

; The probability that X is equal to 7 is:

; 0.0900792