naginterfaces.library.stat.prob_​gamma

naginterfaces.library.stat.prob_gamma(g, a, b, tail='L')[source]

prob_gamma returns the lower or upper tail probability of the gamma distribution, with parameters and .

For full information please refer to the NAG Library document for g01ef

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01eff.html

Parameters
gfloat

, the value of the gamma variate.

afloat

The parameter of the gamma distribution.

bfloat

The parameter of the gamma distribution.

tailstr, length 1, optional

Indicates whether an upper or lower tail probability is required.

The lower tail probability is returned, that is .

The upper tail probability is returned, that is .

Returns
pfloat

The lower or upper tail probability of the gamma distribution, with parameters and .

Raises
NagValueError
(errno )

On entry, .

Constraint: or .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: and .

Warns
NagAlgorithmicWarning
(errno )

The algorithm has failed to converge in iterations. The probability returned should be a reasonable approximation to the solution.

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.

References

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