scipy.special.gammaincinv#

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

Inverse to the regularized lower incomplete gamma function.

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
outndarray, optional: Optional output array for the function values

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 regularized upper 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 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])