naginterfaces.library.stat.prob_​poisson

naginterfaces.library.stat.prob_poisson(rlamda, k)[source]

prob_poisson returns the lower tail, upper tail and point probabilities associated with a Poisson distribution.

For full information please refer to the NAG Library document for g01bk

https://www.nag.com/numeric/nl/nagdoc_28.6/flhtml/g01/g01bkf.html

Parameters
rlamdafloat

The parameter of the Poisson distribution.

kint

The integer which defines the required probabilities.

Returns
plekfloat

The lower tail probability, .

pgtkfloat

The upper tail probability, .

peqkfloat

The point probability, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

Let denote a random variable having a Poisson distribution with parameter . Then

The mean and variance of the distribution are both equal to .

prob_poisson computes for given and the probabilities:

The method is described in Knüsel (1986).

References

Knüsel, L, 1986, Computation of the chi-square and Poisson distribution, SIAM J. Sci. Statist. Comput. (7), 1022–1036