scipy.special.gammainccinv

scipy.special.gammainccinv(a, y) = <ufunc 'gammainccinv'>

Inverse of the upper incomplete gamma function with respect to x

Given an input \(y\) between 0 and 1, returns \(x\) such that \(y = Q(a, x)\). Here \(Q\) is the 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

Returns

scalar or ndarray

Values of the inverse of the upper incomplete gamma function

See also

gammaincc

regularized upper incomplete gamma function

gammainc

regularized lower incomplete gamma function

gammaincinv

inverse of the regularized lower incomplete gamma function with respect to x

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.])