naginterfaces.library.stat.prob_​gamma_​vector

naginterfaces.library.stat.prob_gamma_vector(tail, g, a, b)[source]

prob_gamma_vector returns a number of lower or upper tail probabilities for the gamma distribution.

For full information please refer to the NAG Library document for g01sf

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01sff.html

Parameters
tailstr, length 1, array-like, shape

Indicates whether a lower or upper tail probability is required. For , for :

The lower tail probability is returned, i.e., .

The upper tail probability is returned, i.e., .

gfloat, array-like, shape

, the value of the gamma variate.

afloat, array-like, shape

The parameter of the gamma distribution.

bfloat, array-like, shape

The parameter of the gamma distribution.

Returns
pfloat, ndarray, shape

, the probabilities of the beta distribution.

ivalidint, ndarray, shape

indicates any errors with the input arguments, with

No error.

On entry, invalid value supplied in when calculating .

On entry, .

On entry, , or, .

The solution did not converge in iterations, see specfun.gamma_incomplete for details. The probability returned should be a reasonable approximation to the solution.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of , , or was invalid, or the solution did not converge.

Check for more information.

Notes

The lower tail probability for the gamma distribution with parameters and , , is defined by:

The mean of the distribution is and its variance is . The transformation is applied to yield the following incomplete gamma function in normalized form,

This is then evaluated using specfun.gamma_incomplete.

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

Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth