# scipy.special.gdtrix¶

scipy.special.gdtrix(a, b, p, out=None) = <ufunc 'gdtrix'>

Inverse of gdtr vs x.

Returns the inverse with respect to the parameter x of p = gdtr(a, b, x), the cumulative distribution function of the gamma distribution. This is also known as the p’th quantile of the distribution.

Parameters: a : array_like a parameter values of gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution. b : array_like b parameter values of gdtr(a, b, x). b is the “shape” parameter of the gamma distribution. p : array_like Probability values. out : ndarray, optional If a fourth argument is given, it must be a numpy.ndarray whose size matches the broadcast result of a, b and x. out is then the array returned by the function. x : ndarray Values of the x parameter such that p = gdtr(a, b, x).

gdtr
CDF of the gamma distribution.
gdtria
Inverse with respect to a of gdtr(a, b, x).
gdtrib
Inverse with respect to b of gdtr(a, b, x).

Notes

Wrapper for the CDFLIB [R429] Fortran routine cdfgam.

The cumulative distribution function p is computed using a routine by DiDinato and Morris [R430]. Computation of x involves a seach for a value that produces the desired value of p. The search relies on the monotinicity of p with x.

References

 [R429] (1, 2) Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
 [R430] (1, 2) DiDinato, A. R. and Morris, A. H., Computation of the incomplete gamma function ratios and their inverse. ACM Trans. Math. Softw. 12 (1986), 377-393.

Examples

First evaluate gdtr.

>>> from scipy.special import gdtr, gdtrix
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442


Verify the inverse.

>>> gdtrix(1.2, 3.4, p)
5.5999999999999996