Cdf.Poisson Method

Evaluates the Poisson cumulative probability distribution function.

public static double Poisson(
int k,
double theta
);

Parameters

k: An int specifying the argument for which the Poisson distribution function is to be evaluated.
theta: A double specifying the mean of the Poisson distribution.

Return Value

A double specifying the probability that a Poisson random variable takes a value less than or equal to k.

Remarks

Poisson evaluates the distribution 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 $\theta = theta$ ) is

$f(x) = e^{ - \theta } \theta ^x /x!\,\,\, for\,x = 0,\,1,\,2,\, \ldots$

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

$f\left( {x + 1} \right) = f\left( x \right) (\theta /\left( {x + 1} \right)),\,\,\,for\,x = 0,\,1,\,2,\, \ldots k-1$

with $f(0) = e^{-\theta}$ .

Cdf.Poisson Method

Parameters

Return Value

Remarks

See Also