# scipy.special.gammainccinv#

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

Inverse of the regularized upper incomplete gamma function.

Given an input $$y$$ between 0 and 1, returns $$x$$ such that $$y = Q(a, x)$$. Here $$Q$$ is the regularized upper incomplete gamma function; see gammaincc. This is well-defined because the upper incomplete gamma function is monotonic as can be seen from its definition in [dlmf].

Parameters:
aarray_like

Positive parameter

yarray_like

Argument between 0 and 1, inclusive

outndarray, optional

Optional output array for the function values

Returns:
scalar or ndarray

Values of the inverse of the upper incomplete gamma function

gammaincc

regularized upper incomplete gamma function

gammainc

regularized lower incomplete gamma function

gammaincinv

inverse of the regularized lower incomplete gamma function

References

[dlmf]

NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/8.2#E4

Examples

>>> import scipy.special as sc


It starts at infinity and monotonically decreases to 0.

>>> sc.gammainccinv(0.5, [0, 0.1, 0.5, 1])
array([       inf, 1.35277173, 0.22746821, 0.        ])


It inverts the upper incomplete gamma function.

>>> a, x = 0.5, [0, 0.1, 0.5, 1]
>>> sc.gammaincc(a, sc.gammainccinv(a, x))
array([0. , 0.1, 0.5, 1. ])

>>> a, x = 0.5, [0, 10, 50]
>>> sc.gammainccinv(a, sc.gammaincc(a, x))
array([ 0., 10., 50.])