scipy.special.gdtrib#

scipy.special.gdtrib(a, p, x, out=None) = <ufunc 'gdtrib'>#

Inverse of gdtr vs b.

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

Parameters

aarray_like: a parameter values of gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution.
parray_like: Probability values.
xarray_like: Nonnegative real values, from the domain of the gamma distribution.
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

bndarray: Values of the b parameter such that p = gdtr(a, b, x). b is the “shape” parameter of the gamma distribution.

See also

gdtr: CDF of the gamma distribution.
gdtria: Inverse with respect to a of gdtr(a, b, x).
gdtrix: Inverse with respect to x 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 b involves a search for a value that produces the desired value of p. The search relies on the monotonicity of p with b.

References

1: Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
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, gdtrib
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442

Verify the inverse.

>>> gdtrib(1.2, p, 5.6)
3.3999999999723882

scipy.special.gdtria

scipy.special.gdtrix