poisson_pdf

Evaluates the Poisson probability function.

Synopsis

#include <imsls.h>

float imsls_f_poisson_pdf (int k, float theta)

The type double function is imsls_d_poisson_pdf.

Required Arguments

int k (Input)
Argument for which the Poisson distribution function is to be evaluated.

floattheta (Input)
Mean of the Poisson distribution. theta must be positive.

Return Value

Function value, the probability that a Poisson random variable takes a value equal to k.

Description

Function imsls_f_poisson_pdf evaluates the probability 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 θ = theta) is

f(x|θ) = e-θ θk/k!,      for k = 0, 1, 2,...

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

 

Figure 1,  Poisson Probability Function

Example

Suppose X is a Poisson random variable with θ = 10. In this example, we evaluate the probability function at 7.

 

#include <imsls.h>

#include <stdio.h>

 

int main () {

    int   k = 7;

    float theta = 10.0;

 

    printf ("The probability that X is equal to %d is %g.\n",

        k, imsls_f_poisson_pdf (k, theta));

}

Output

 

The probability that X is equal to 7 is 0.0900792.