scipy.special.gammaincinv

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

Inverse to the lower incomplete gamma function with respect to x.

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

Parameters

aarray_like

Positive parameter

yarray_like

Parameter between 0 and 1, inclusive

Returns

scalar or ndarray

Values of the inverse of the lower incomplete gamma function

See also

gammainc

regularized lower incomplete gamma function

gammaincc

regularized upper incomplete gamma function

gammainccinv

inverse of the regualizred upper 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 0 and monotonically increases to infinity.

>>> sc.gammaincinv(0.5, [0, 0.1 ,0.5, 1])
array([0.        , 0.00789539, 0.22746821,        inf])

It inverts the lower incomplete gamma function.

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

>>> a, x = 0.5, [0, 10, 25]
>>> sc.gammaincinv(a, sc.gammainc(a, x))
array([ 0.        , 10.        , 25.00001465])