naginterfaces.library.stat.prob_​beta

naginterfaces.library.stat.prob_beta(x, a, b)[source]

prob_beta computes the upper and lower tail probabilities and the probability density function of the beta distribution with parameters and .

For full information please refer to the NAG Library document for g01ee

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01eef.html

Parameters
xfloat

, the value of the beta variate.

afloat

, the first parameter of the required beta distribution.

bfloat

, the second parameter of the required beta distribution.

Returns
pfloat

The lower tail probability, .

qfloat

The upper tail probability, .

pdffloat

The probability density function, .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, and .

Constraint: .

Notes

The probability density function of the beta distribution with parameters and is:

The lower tail probability, is defined by

The function , also known as the incomplete beta function is calculated using specfun.beta_incomplete.

References

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