Evaluates the Poisson distribution function.
Synopsis
#include <imsl.h>
float imsl_f_poisson_cdf (int k, float theta)
The type double function is imsl_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
The function imsl_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
f(x) = e-q θx/x!, for x = 0, 1, 2, ¼
The individual terms are calculated from the tails of the distribution to the mode of the distribution and summed. The function imsl_f_poisson_cdf uses the recursive relationship
f(x + 1) = f(x)q/(x + 1), for x = 0, 1, 2, ¼, k - 1
with f(0) = e-q.
Figure 9-3 Plot of Fp(k, θ)
Example
Suppose X is a Poisson random variable with θ = 10. This example evaluates the probability that X ≤ 7.
#include <imsl.h>
void
main()
{
int k = 7;
float theta = 10.0;
float p;
p =
imsl_f_poisson_cdf(k, theta);
printf("Pr(x <= 7) =
%6.4f\n", p);
}
Output
Pr(x <= 7) = 0.2202
Informational Errors
IMSL_LESS_THAN_ZERO The input argument, k, is less than zero.
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