>  Docs Center  >  IDL Reference  >  Advanced Math and Stats  >  IMSL_POISSONCDF

IMSL_POISSONCDF

IMSL_POISSONCDF

The IMSL_POISSONCDF function evaluates the Poisson distribution function.

This routine requires an IDL Advanced Math and Stats license. For more information, contact your 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) = (eθx)/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

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

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 (optional)

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


IMSL_POISSON2D



© 2019 Harris Geospatial Solutions, Inc. |  Legal
My Account    |    Store    |    Contact Us