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.
Argument for which the Poisson distribution function is to be evaluated.
floattheta (Input)
Mean of the Poisson distribution. theta must be positive.
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 12, 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.
