scipy.special.betainccinv — SciPy v1.15.2 Manual (original) (raw)
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 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
regularized incomplete beta function
complement of the regularized incomplete beta function
Notes
Added in version 1.11.0.
This function wraps the ibetac_inv routine from the Boost Math C++ library [2].
References
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