Cdf.Poisson Method

CdfPoisson Method

Evaluates the Poisson cumulative probability distribution function.

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

public static double Poisson(
	int k,
	double theta
)

Public Shared Function Poisson ( 
	k As Integer,
	theta As Double
) As Double

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

static member Poisson : 
        k : int * 
        theta : float -> float

Parameters

k: Type: SystemInt32
The int argument for which the Poisson distribution function is to be evaluated.
theta: Type: SystemDouble
A double scalar value representing the mean of the Poisson distribution.

Return Value

Type: Double
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 $f(0)=e^{-\theta}$ .

Reference

Cdf Class

Imsl.Stat Namespace

Other Resources

Example