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

See also

betainc

regularized incomplete beta function

betaincc

complement of the regularized incomplete beta function

Notes

Added in version 1.11.0.

References

[1]

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

Examples

Try it in your browser!

>>> 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

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