# 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 [1] Fortran routine cdfgam.

The cumulative distribution function p is computed using a routine by DiDinato and Morris [2]. 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

[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, gdtria
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442
```

Verify the inverse.

```>>> gdtria(p, 3.4, 5.6)
1.2
```