naginterfaces.library.stat.inv_​cdf_​beta_​vector

naginterfaces.library.stat.inv_cdf_beta_vector(tail, p, a, b, tol=0.0)[source]

inv_cdf_beta_vector returns a number of deviates associated with given probabilities of the beta distribution.

For full information please refer to the NAG Library document for g01te

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01tef.html

Parameters
tailstr, length 1, array-like, shape

Indicates which tail the supplied probabilities represent. For , for :

The lower tail probability, i.e., .

The upper tail probability, i.e., .

pfloat, array-like, shape

, the probability of the required beta distribution as defined by .

afloat, array-like, shape

, the first parameter of the required beta distribution.

bfloat, array-like, shape

, the second parameter of the required beta distribution.

tolfloat, optional

The relative accuracy required by you in the results. If inv_cdf_beta_vector is entered with greater than or equal to or less than (see machine.precision), the value of is used instead.

Returns
betafloat, ndarray, shape

, the deviates 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, , or, , or, .

The solution has not converged but the result should be a reasonable approximation to the solution.

Requested accuracy not achieved when calculating the beta probability. The result should be a reasonable approximation to the correct 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 failed to converge.

Check for more information.

Notes

The deviate, , associated with the lower tail probability, , of the beta distribution with parameters and is defined as the solution to

The algorithm is a modified version of the Newton–Raphson method, following closely that of Cran et al. (1977).

An initial approximation, , to is found (see Cran et al. (1977)), and the Newton–Raphson iteration

where is used, with modifications to ensure that remains in the range .

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

Cran, G W, Martin, K J and Thomas, G E, 1977, Algorithm AS 109. Inverse of the incomplete beta function ratio, Appl. Statist. (26), 111–114

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