Random.NextPoisson Method

Generate a pseudorandom number from a Poisson distribution.

public virtual int NextPoisson(
double theta
);

Parameters

theta: A double which specifies the mean of the Poisson distribution, $theta \gt 0$ .

Return Value

A int which specifies a pseudorandom number from a Poisson distribution.

Remarks

Method NextPoisson generates pseudorandom numbers from a Poisson distribution with parameter theta. theta, which is the mean of the Poisson random variable, must be positive. The probability function (with $\rm \theta = theta$ ) is

$f(x) = e^{ - {\rm{\theta}}} \, {\rm{\theta}}^{x} /x !$

for $x = 0, 1, 2, \ldots$

If theta is less than 15, NextPoisson uses an inverse CDF method; otherwise the PTPE method of Schmeiser and Kachitvichyanukul (1981) (see also Schmeiser 1983) is used.

The PTPE method uses a composition of four regions, a triangle, a parallelogram, and two negative exponentials. In each region except the triangle, acceptance/rejection is used. The execution time of the method is essentially insensitive to the mean of the Poisson.

Random.NextPoisson Method

Parameters

Return Value

Remarks

See Also