IDL Analyst Reference Guide: Probability Distribution Functions and Inverses

IMSL_BINOMIALCDF

The IMSL_BINOMIALCDF function evaluates the binomial distribution function.

Syntax

Result = IMSL_BINOMIALCDF(k, n, p [, /DOUBLE])

Return Value

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

Arguments

k

Argument for which the binomial distribution function is to be evaluated.

n

Number of Bernoulli trials.

p

Probability of success on each trial.

Keywords

DOUBLE

If present and nonzero, double precision is used.

Discussion

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

To avoid the possibility of underflow, the probabilities are computed forward from 0 if k is not greater than n times p; otherwise, they are computed backward from n. The smallest positive machine number, e, is used as the starting value for summing the probabilities, which are rescaled by (1 – p)ⁿe if forward computation is performed and by pⁿe if backward computation is done.

For the special case of p = 0, IMSL_BINOMIALCDF is set to 1; for the case p = 1, IMSL_BINOMIALCDF is set to 1 if k = n and is set to zero otherwise.

Example

Suppose X is a binomial random variable with n = 5 and p = 0.95. This example finds the probability that X is less than or equal to 3.

p = IMSL_BINOMIALCDF(3, 5, .95)  
PM, 'Pr(x < 3) = ', p, FORMAT = '(a12, f7.4)'  
  
Pr(x < 3) =  0.0226