# naginterfaces.library.stat.prob_​poisson_​vector¶

naginterfaces.library.stat.prob_poisson_vector(l, k)[source]

prob_poisson_vector returns a number of the lower tail, upper tail and point probabilities for the Poisson distribution.

For full information please refer to the NAG Library document for g01sk

https://www.nag.com/numeric/nl/nagdoc_29/flhtml/g01/g01skf.html

Parameters
lfloat, array-like, shape

, the parameter of the Poisson distribution.

kint, array-like, shape

, the integer which defines the required probabilities.

Returns
plekfloat, ndarray, shape

, the lower tail probabilities.

pgtkfloat, ndarray, shape

, the upper tail probabilities.

peqkfloat, ndarray, shape

, the point probabilities.

ivalidint, ndarray, shape

indicates any errors with the input arguments, with

No error.

On entry, .

On entry, .

On entry, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of or was invalid.

Notes

Let denote a vector of random variables each having a Poisson distribution with parameter . Then

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

prob_poisson_vector computes, for given and the probabilities: , and using the algorithm described in Knüsel (1986).

The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See the G01 Introduction for further information.

References

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