scipy.special.gdtrib#
- scipy.special.gdtrib(a, p, x, out=None) = <ufunc 'gdtrib'>#
- Inverse of - gdtrvs 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/ais 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:
- bscalar or ndarray
- Values of the b parameter such that p = gdtr(a, b, x). b is the “shape” parameter of the gamma distribution. 
 
 - See also - Notes - The cumulative distribution function p is computed using the Cephes [1] routines igam and igamc. Computation of b involves a search for a value that produces the desired value of p using Chandrupatla’s bracketing root finding algorithm [2]. - Note that there are some edge cases where - gdtribis extended by taking limits where they are uniquely defined. In particular- x == 0with- p > 0and- p == 0with- x > 0. For these edge cases, a numerical result will be returned for- gdtrib(a, p, x)even though- gdtr(a, gdtrib(a, p, x), x)is undefined.- References [1]- Cephes Mathematical Functions Library, http://www.netlib.org/cephes/ [2]- Chandrupatla, Tirupathi R. “A new hybrid quadratic/bisection algorithm for finding the zero of a nonlinear function without using derivatives”. Advances in Engineering Software, 28(3), 145-149. https://doi.org/10.1016/s0965-9978(96)00051-8 - 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) 3.3999999999999995