binomial_cdf

Evaluates the binomial distribution function.

Synopsis

#include <imsl.h>

float imsl_f_binomial_cdf (int k, int n, float p)

The type double function is imsl_d_binomial_cdf.

Required Arguments

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

int n (Input)
Number of Bernoulli trials.

float p (Input)
Probability of success on each trial.

Return Value

The probability that k or fewer successes occur in n independent Bernoulli trials, each of which has a probability p of success.

Description

The function imsl_f_binomial_cdf evaluates the distribution function of a binomial random variable with parameters n and p. It does this by summing probabilities of the random variable taking on the specific values in its range. These probabilities are computed by the recursive relationship

 

To avoid the possibility of underflow, the probabilities are computed forward from zero if k is not greater than n × p; otherwise, they are computed backward from n. The smallest positive machine number, ɛ, is used as the starting value for summing the probabilities, which are rescaled by (1 − p)n ɛ if forward computation is performed and by pnɛ if backward computation is done.

For the special case of p is zero, imsl_f_binomial_cdf is set to 1; and for the case p is 1, imsl_f_binomial_cdf is set to 1 if k = n and is set to zero otherwise.

Example

Suppose X is a binomial random variable with an n = 5 and a p = 0.95. This example finds the probability that X is less than or equal to three.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

int k = 3;

int n = 5;

float p = 0.95;

float pr;

 

pr = imsl_f_binomial_cdf(k,n,p);

printf("Pr(x <= 3) = %6.4f\n", pr);

}

Output

 

Pr(x <= 3) = 0.0226

Informational Errors

IMSL_LESS_THAN_ZERO	The input argument, k, is less than zero.
IMSL_GREATER_THAN_N	The input argument, k, is greater than the number of Bernoulli trials, n.