Module « scipy.special »

Fonction gammainc - module scipy.special

Signature de la fonction gammainc

Description

gammainc.__doc__

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

gammainc(a, x)

Regularized lower incomplete gamma function.

It is defined as

.. math::

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

for :math:`a > 0` and :math:`x \geq 0`. See [dlmf]_ for details.

Parameters
----------
a : array_like
    Positive parameter
x : array_like
    Nonnegative argument

Returns
-------
scalar or ndarray
    Values of the lower incomplete gamma function

Notes
-----
The function satisfies the relation ``gammainc(a, x) +
gammaincc(a, x) = 1`` where `gammaincc` is the regularized upper
incomplete gamma function.

The implementation largely follows that of [boost]_.

See also
--------
gammaincc : regularized upper incomplete gamma function
gammaincinv : inverse of the regularized lower incomplete gamma
    function with respect to `x`
gammainccinv : inverse of the regularized upper incomplete gamma
    function with respect to `x`

References
----------
.. [dlmf] NIST Digital Library of Mathematical functions
          https://dlmf.nist.gov/8.2#E4
.. [boost] Maddock et. al., "Incomplete Gamma Functions",
   https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html

Examples
--------
>>> import scipy.special as sc

It is the CDF of the gamma distribution, so it starts at 0 and
monotonically increases to 1.

>>> sc.gammainc(0.5, [0, 1, 10, 100])
array([0.        , 0.84270079, 0.99999226, 1.        ])

It is equal to one minus the upper incomplete gamma function.

>>> a, x = 0.5, 0.4
>>> sc.gammainc(a, x)
0.6289066304773024
>>> 1 - sc.gammaincc(a, x)
0.6289066304773024