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Module « scipy.special »

Fonction gdtrib - module scipy.special

Signature de la fonction gdtrib

def gdtrib(*args, **kwargs) 

Description

help(scipy.special.gdtrib)

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

gdtrib(a, p, x, out=None)

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 : scalar or 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)`.

Notes
-----

The cumulative distribution function `p` is computed using the Cephes [1]_
routines `igam` and `igamc`. Computation of `b` involves a search for a value
that produces the desired value of `p` using Chandrupatla's bracketing
root finding algorithm [2]_.

Note that there are some edge cases where `gdtrib` is extended by taking
limits where they are uniquely defined. In particular
``x == 0`` with ``p > 0`` and ``p == 0`` with ``x > 0``.
For these edge cases, a numerical result will be returned for
``gdtrib(a, p, x)`` even though ``gdtr(a, gdtrib(a, p, x), x)`` is
undefined.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/
.. [2] Chandrupatla, Tirupathi R.
       "A new hybrid quadratic/bisection algorithm for finding the zero of a
       nonlinear function without using derivatives".
       Advances in Engineering Software, 28(3), 145-149.
       https://doi.org/10.1016/s0965-9978(96)00051-8

Examples
--------
First evaluate `gdtr`.

>>> from scipy.special import gdtr, gdtrib
>>> p = gdtr(1.2, 3.4, 5.6)
>>> print(p)
0.94378087442

Verify the inverse.

>>> gdtrib(1.2, p, 5.6)
3.3999999999999995

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