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) = (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
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 |