naginterfaces.library.stat.prob_​beta_​vector

naginterfaces.library.stat.prob_beta_vector(tail, beta, a, b)[source]

prob_beta_vector computes a number of lower or upper tail probabilities for the beta distribution.

For full information please refer to the NAG Library document for g01se

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01sef.html

Parameters
tailstr, length 1, array-like, shape

Indicates whether a lower or upper tail probabilities are required. For , for :

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

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

betafloat, array-like, shape

, the value of the beta variate.

afloat, array-like, shape

, the first parameter of the required beta distribution.

bfloat, array-like, shape

, the second parameter of the required beta distribution.

Returns
pfloat, ndarray, shape

, the probabilities for 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, , or, .

On entry, , or, .

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.

Check for more information.

Notes

The lower tail probability, is defined by

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

NIST Digital Library of Mathematical Functions

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

Majumder, K L and Bhattacharjee, G P, 1973, Algorithm AS 63. The incomplete beta integral, Appl. Statist. (22), 409–411