# 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:
parray_like

Probability values.

barray_like

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

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:
ascalar or ndarray

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

`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  Fortran routine cdfgam.

The cumulative distribution function p is computed using a routine by DiDinato and Morris . 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



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



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
```