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.])

scipy.special.gammaincc scipy.special.beta