Module « scipy.special »

Fonction gdtr - module scipy.special

Signature de la fonction gdtr

Description

gdtr.__doc__

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

gdtr(a, b, x)

Gamma distribution cumulative distribution function.

Returns the integral from zero to `x` of the gamma probability density
function,

.. math::

    F = \int_0^x \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,

where :math:`\Gamma` is the gamma function.

Parameters
----------
a : array_like
    The rate parameter of the gamma distribution, sometimes denoted
    :math:`\beta` (float).  It is also the reciprocal of the scale
    parameter :math:`\theta`.
b : array_like
    The shape parameter of the gamma distribution, sometimes denoted
    :math:`\alpha` (float).
x : array_like
    The quantile (upper limit of integration; float).

See also
--------
gdtrc : 1 - CDF of the gamma distribution.

Returns
-------
F : ndarray
    The CDF of the gamma distribution with parameters `a` and `b`
    evaluated at `x`.

Notes
-----
The evaluation is carried out using the relation to the incomplete gamma
integral (regularized gamma function).

Wrapper for the Cephes [1]_ routine `gdtr`.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/