IMSL_POISSONCDF

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Errors | Version History

The IMSL_POISSONCDF function evaluates the Poisson 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_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.

Discussion

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:

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:

,

with

.

Example

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 

Errors

Informational Errors

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

Version History