Evaluates the Poisson probability density 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
An int scalar for which the Poisson probability 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 equal to k.

Remarks

Method Pdf.Poisson evaluates the probability density 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 ^k /k!,\,\,\,\,\, for\,\,\,\, k = 0,\,\,1,\,\,2,\, \ldots

Pdf.Poisson evaluates this function directly, taking logarithms and using the log gamma function.

Poisson ProbabilityFunction

See Also