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

aarray_like

a parameter values of gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution.

barray_like

b parameter values of gdtr(a, b, x). b is the “shape” parameter of the gamma distribution.

parray_like

Probability values.

outndarray, 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.

Returns

xndarray

Values of the x parameter such that p = gdtr(a, b, x).

See also

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 [1] Fortran routine cdfgam.

The cumulative distribution function p is computed using a routine by DiDinato and Morris [2]. Computation of x involves a search for a value that produces the desired value of p. The search relies on the monotonicity of p with x.

References

1(1,2)

Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.

2(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