poisson_cdf

Evaluates the Poisson distribution function.

Synopsis

#include <imsls.h>

float imsls_f_c (int k, float theta)

The type double function is imsls_d_poisson_cdf.

Required Arguments

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

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

Return Value

The probability that a Poisson random variable takes a value less than or equal to k.

Description

Function imsls_f_poisson_cdf evaluates the distribution function of a Poisson random variable with parameter theta. The mean of the Poisson random variable, theta, must be positive. The probability function (with θ = theta) is as follows:

 

The individual terms are calculated from the tails of the distribution to the mode of the distribution and summed. Function imsls_f_poisson_cdf uses the recursive relationship

 

with f (0) = e-q.

 

Figure 1,  Plot of Fp (k, θ)

Example

Suppose X is a Poisson random variable with θ = 10. In this example, we evaluate the probability that X is less than or equal to 7.

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

    int    k = 7;

    float  theta = 10.0, p;

 

    p = imsls_f_poisson_cdf(k, theta);

    printf("Pr(x <= %d) = %6.4f\n", k, p);

}

 

Output

 

Pr(x <= 7) = 0.2202

Informational Errors

IMSLS_LESS_THAN_ZERO

Since “k” = # is less than zero, the distribution function is set to zero.