scipy.special.gdtria¶

scipy.special.gdtria(p, b, x, out=None) = <ufunc 'gdtria'>¶

Inverse of gdtr vs a.

Returns the inverse with respect to the parameter a of p = gdtr(a, b, x), the cumulative distribution function of the gamma distribution.

Parameters:

Parameters:	p : array_like Probability values. b : array_like b parameter values of gdtr(a, b, x). b is the “shape” parameter of the gamma distribution. x : array_like Nonnegative real values, from the domain of the gamma distribution. 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.
Returns:	a : ndarray Values of the a parameter such that p = gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution.

p : array_like

Probability values.

b : array_like

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

x : array_like

Nonnegative real values, from the domain of the gamma distribution.

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.

Returns:

a : ndarray

Values of the a parameter such that p = gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution.

See also

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

Notes

Wrapper for the CDFLIB [R441] Fortran routine cdfgam.

The cumulative distribution function p is computed using a routine by DiDinato and Morris [R442]. Computation of a involves a search for a value that produces the desired value of p. The search relies on the monotonicity of p with a.

References

[R441]

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

[R442]

(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, gdtria
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442

Verify the inverse.

>>> gdtria(p, 3.4, 5.6)
1.2