scipy.special.betaincinv

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

Inverse of the 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 incomplete beta function

See also

betainc

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