# 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-θθx)/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

6.4 | Introduced

## See Also