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The IMSL_POISSONCDF function evaluates the Poisson distribution function.

The IMSL_POISSONCDF function 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:

f(x) = (e-θθx)/x! for x = 0, 1, 2, ...

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

f(x + 1) = f(x)(θ/(x + 1)), for x = 0, 1, 2, ..., k - 1


f(0) = e-θ

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