# scipy.special.betainccinv#

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

Inverse of the complemented regularized incomplete beta function.

Computes $$x$$ such that:

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

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

betaincc

complement of the regularized incomplete beta function

Notes

References

[1]

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

Examples

>>> from scipy.special import betainccinv, betaincc

This function is the inverse of betaincc for fixed values of $$a$$ and $$b$$.

>>> a, b = 1.2, 3.1
>>> y = betaincc(a, b, 0.2)
>>> betainccinv(a, b, y)
0.2
>>> a, b = 7, 2.5
>>> x = betainccinv(a, b, 0.875)
>>> betaincc(a, b, x)
0.875