# scipy.special.betaincinv#

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 betainc and $$\Gamma$$ 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

betainc

regularized incomplete beta function

gamma

gamma function

References

[1]

NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/8.17

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