maxframe.tensor.special.betaincinv#

maxframe.tensor.special.betaincinv(a, b, y, out=None, **kwargs)[source]#

Inverse of the regularized incomplete beta function.

Computes \(x\) such that:

\[y = I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x t^{a-1}(1-t)^{b-1}dt,\]

where \(I_x\) is the normalized incomplete beta function betainc and \(\Gamma\) is the gamma function [1].

Parameters:

  • a (array_like) – Positive, real-valued parameters

  • b (array_like) – Positive, real-valued parameters

  • y (array_like) – Real-valued input

  • out (ndarray, optional) – Optional output array for function values

Returns:

Value of the inverse of the regularized incomplete beta function

Return type:

scalar or ndarray

See also

betainc

regularized incomplete beta function

gamma

gamma function

Notes

This function wraps the ibeta_inv routine from the Boost Math C++ library [2].

References