BINOMIAL

The BINOMIAL function computes the probability that in a cumulative binomial ( Bernoulli) distribution, a random variable X is greater than or equal to a user-specified value V , given N independent performances and a probability of occurrence or success P in a single performance.

This routine is written in the IDL language. Its source code can be found in the file binomial.pro in the lib subdirectory of the IDL distribution.

Calling Sequence

Result = BINOMIAL( V, N, P )

Arguments

V

A non-negative integer specifying the minimum number of times the event occurs in N independent performances.

N

A non-negative integer specifying the number of performances. If the number of performances exceeds 25, the Gaussian distribution is used to approximate the cumulative binomial distribution.

P

A non-negative single- or double-precision floating-point scalar, in the interval [0.0, 1.0], that specifies the probability of occurrence or success of a single independent performance.

Examples

Compute the probability of obtaining at least two 6s in rolling a die four times. The result should be 0.131944.

result = binomial(2, 4, 1.0/6.0)

Compute the probability of obtaining exactly two 6s in rolling a die four times. The result should be 0.115741.

result = binomial(2, 4, 1./6.) - binomial(3, 4, 1./6.)

Compute the probability of obtaining three or fewer 6s in rolling a die four times. The result should be 0.999228.

result = (binomial(0, 4, 1./6.) - binomial(1, 4, 1./6.)) + $

(binomial(1, 4, 1./6.) - binomial(2, 4, 1./6.)) + $

(binomial(2, 4, 1./6.) - binomial(3, 4, 1./6.)) + $

(binomial(3, 4, 1./6.) - binomial(4, 4, 1./6.))

See Also

CHISQR_PDF , F_PDF , GAUSS_PDF , T_PDF