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.
Argument for which the Poisson distribution function is to be evaluated.
float theta (Input)
Mean of the Poisson distribution. Argument theta must be positive.
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 11, 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. |
