scipy.special.betaincinv — SciPy v1.15.3 Manual (original) (raw)

scipy.special.betaincinv(a, b, y, out=None) = <ufunc 'betaincinv'>#

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 betaincand \(\Gamma\) is the gamma function [1].

Parameters:

a, barray_like

Positive, real-valued parameters

yarray_like

Real-valued input

outndarray, optional

Optional output array for function values

Returns:

scalar or ndarray

Value of the inverse of the regularized incomplete beta function

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

Examples

import scipy.special as sc

This function is the inverse of betainc for fixed values of \(a\) and \(b\).

a, b = 1.2, 3.1 y = sc.betainc(a, b, 0.2) sc.betaincinv(a, b, y) 0.2

a, b = 7.5, 0.4 x = sc.betaincinv(a, b, 0.5) sc.betainc(a, b, x) 0.5