IMSL_POISSONCDF

The IMSL_POISSONCDF function evaluates the Poisson distribution function.

Note: This routine requires an IDL Analyst license. For more information, contact your Exelis VIS sales or technical support representative.

The IMSL_POISSONCDF function evaluates the distribution function of a Poisson random variable with parameter theta. The mean of the Poisson random variable, theta, must be positive.

The probability function (with θ = theta) is as follows:

f(x) = (e^-θθ^x)/x! for x = 0, 1, 2, ...

The individual terms are calculated from the tails of the distribution to the mode of the distribution and summed. The IMSL_POISSONCDF function uses the recursive relationship:

f(x + 1) = f(x)(θ/(x + 1)), for x = 0, 1, 2, ..., k - 1

with:

f(0) = e^-θ

Examples

Example 1

Suppose X is a Poisson random variable with θ = 10. This example evaluates the probability that X ≤ 7.

p = IMSL_POISSONCDF(7, 10)

PM, 'Pr(x <= 7) = ', p, FORMAT = '(a13,f7.4)'

Pr(x <= 7) = 0.2202

Syntax

Result = IMSL_POISSONCDF(k, theta [, /DOUBLE] )

Return Value

The probability that a Poisson random variable takes a value less than or equal to k.

Arguments

k

Parameter for which the Poisson distribution function is to be evaluated.

theta

Mean of the Poisson distribution. Parameter theta must be positive.

Keywords

DOUBLE

If present and nonzero, double precision is used.

Errors

Informational Errors

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

Version History

See Also