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 pth 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
- xscalar or ndarray
Values of the x parameter such that p = gdtr(a, b, x).
See also
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
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, gdtrix >>> p = gdtr(1.2, 3.4, 5.6) >>> print(p) 0.94378087442
Verify the inverse.
>>> gdtrix(1.2, 3.4, p) 5.5999999999999996