# 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
xndarray

Values of the x parameter such that p = gdtr(a, b, x).

`gdtr`

CDF of the gamma distribution.

`gdtria`

Inverse with respect to a of gdtr(a, b, x).

`gdtrib`

Inverse with respect to b 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 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
```