IMSL_BINOMIALCDF

The IMSL_BINOMIALCDF function evaluates the binomial distribution function.

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

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, ε, is used as the starting value for summing the probabilities, which are rescaled by (1 – p)ⁿε if forward computation is performed and by pⁿε 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

Errors

Informational Errors

STAT_LESS_THAN_ZERO—Input parameter, k, is less than zero.

STAT_GREATER_THAN_N—Input parameter, k, is greater than the number of Bernoulli trials, n.

Version History


6.4	Introduced