SciPy

scipy.special.gdtrib

scipy.special.gdtrib(a, p, x, out=None) = <ufunc 'gdtrib'>

Inverse of gdtr vs 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 :

a : array_like

a parameter values of gdtr(a, b, x). 1/a is the “scale” parameter of the gamma distribution.

p : array_like

Probability values.

x : array_like

Nonnegative real values, from the domain of the gamma distribution.

out : ndarray, 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 :

b : ndarray

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

See also

gdtr
CDF of the gamma distribution.
gdtria
Inverse with respect to a of gdtr(a, b, x).
gdtrix
Inverse with respect to x of gdtr(a, b, x).

Examples

First evaluate gdtr.

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

Verify the inverse.

>>> gdtrib(1.2, p, 5.6)
3.3999999999723882

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