binomial_pdf

Evaluates the binomial probability function.

Synopsis

#include <imsls.h>

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

The type double function is imsls_d_binomial_pdf.

Required Arguments

int k (Input)
Argument for which the binomial probability 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 a binomial random variable takes on a value equal to k.

Description

The function imsls_f_binomial_pdf evaluates the probability that a binomial random variable with parameters n and p takes on the value k. Specifically,

 

where k = {0,1,2,…,n}, n≥1, 0≤p≤1, and

 

These probabilities are computed by the recursive relationship:

 

To avoid the possibility of underflow, the probabilities are computed forward from 0, if k is not greater than n × p, and are computed backward from n otherwise. The smallest positive machine number, ɛ, is used as the starting value for summing the probabilities, which are rescaled by (1-p)nɛ if forward computation is performed and by pnɛ if backward computation is done.

For the special case of p = 0, imsls_f_binomial_pdf is set to 0 if k is greater than 0 and to 1 otherwise; and for the case p = 1, imsls_f_binomial_pdf is set to 0 if k is less than n and to 1 otherwise.

Examples

Suppose X is a binomial random variable with n = 5 and p = 0.95. In this example, we find the probability that X is equal to 3.

 

#include <stdio.h>

#include <imsls.h>

 

int main()

{

    int k = 3, n = 5;

    float p = 0.95, prob;

 

    prob = imsls_f_binomial_pdf(k, n, p);

    printf("The probability that X is equal to "

        "%d is %f\n", k, prob);

}

Output

 

The probability that X is equal to 3 is 0.021434