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:

Returns:

scalar or ndarray: Value of the inverse of the regularized incomplete beta function

See also

Notes

Added in version 1.11.0.

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

References

[1]

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

[2]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

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