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

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  Fortran routine cdfgam.

The cumulative distribution function p is computed using a routine by DiDinato and Morris . 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, 2) Barry Brown, James Lovato, and Kathy Russell, CDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.
  (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, gdtrib
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442


Verify the inverse.

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


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