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://support.nag.com/numeric/nl/nagdoc_30.3/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