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Module « scipy.special »

Fonction gammaincc - module scipy.special

Signature de la fonction gammaincc

def gammaincc(*args, **kwargs) 

Description

help(scipy.special.gammaincc)

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


    gammaincc(a, x, out=None)

    Regularized upper incomplete gamma function.

    It is defined as

    .. math::

        Q(a, x) = \frac{1}{\Gamma(a)} \int_x^\infty 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
    out : ndarray, optional
        Optional output array for the function values

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

    See Also
    --------
    gammainc : regularized lower incomplete gamma function
    gammaincinv : inverse of the regularized lower incomplete gamma function
    gammainccinv : inverse of the regularized upper incomplete gamma function

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

    The implementation largely follows that of [boost]_.

    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 survival function of the gamma distribution, so it
    starts at 1 and monotonically decreases to 0.

    >>> sc.gammaincc(0.5, [0, 1, 10, 100, 1000])
    array([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,
           0.00000000e+00])

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

    >>> a, x = 0.5, 0.4
    >>> sc.gammaincc(a, x)
    0.37109336952269756
    >>> 1 - sc.gammainc(a, x)
    0.37109336952269756
    

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