Evaluates the Poisson cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static double Poisson(
	int k,
	double theta
)
Visual Basic (Declaration)
Public Shared Function Poisson ( _
	k As Integer, _
	theta As Double _
) As Double
Visual C++
public:
static double Poisson(
	int k, 
	double theta
)

Parameters

k
Type: System..::.Int32
The int argument for which the Poisson distribution function is to be evaluated.
theta
Type: System..::.Double
A double scalar value representing the mean of the Poisson distribution.

Return Value

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

Remarks

Cdf.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!\,\,\,\,\,\mbox{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. Cdf.Poisson uses the recursive relationship

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

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

See Also