Module « scipy.special »

Fonction gdtrix - module scipy.special

Signature de la fonction gdtrix

Description

gdtrix.__doc__

gdtrix(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

gdtrix(a, b, p, out=None)

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
----------
a : array_like
    `a` parameter values of `gdtr(a, b, x)`. `1/a` is the "scale"
    parameter of the gamma distribution.
b : array_like
    `b` parameter values of `gdtr(a, b, x)`. `b` is the "shape" parameter
    of the gamma distribution.
p : array_like
    Probability values.
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
-------
x : ndarray
    Values of the `x` parameter such that `p = gdtr(a, b, x)`.

See Also
--------
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 [1]_ Fortran routine `cdfgam`.

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