Module « scipy.stats »

Fonction kstatvar - module scipy.stats

Signature de la fonction kstatvar

def kstatvar(data, n=2) 

Description

kstatvar.__doc__

Return an unbiased estimator of the variance of the k-statistic.

    See `kstat` for more details of the k-statistic.

    Parameters
    ----------
    data : array_like
        Input array. Note that n-D input gets flattened.
    n : int, {1, 2}, optional
        Default is equal to 2.

    Returns
    -------
    kstatvar : float
        The nth k-statistic variance.

    See Also
    --------
    kstat: Returns the n-th k-statistic.
    moment: Returns the n-th central moment about the mean for a sample.

    Notes
    -----
    The variances of the first few k-statistics are given by:

    .. math::

        var(k_{1}) = \frac{\kappa^2}{n}
        var(k_{2}) = \frac{\kappa^4}{n} + \frac{2\kappa^2_{2}}{n - 1}
        var(k_{3}) = \frac{\kappa^6}{n} + \frac{9 \kappa_2 \kappa_4}{n - 1} +
                     \frac{9 \kappa^2_{3}}{n - 1} +
                     \frac{6 n \kappa^3_{2}}{(n-1) (n-2)}
        var(k_{4}) = \frac{\kappa^8}{n} + \frac{16 \kappa_2 \kappa_6}{n - 1} +
                     \frac{48 \kappa_{3} \kappa_5}{n - 1} +
                     \frac{34 \kappa^2_{4}}{n-1} + \frac{72 n \kappa^2_{2} \kappa_4}{(n - 1) (n - 2)} +
                     \frac{144 n \kappa_{2} \kappa^2_{3}}{(n - 1) (n - 2)} +
                     \frac{24 (n + 1) n \kappa^4_{2}}{(n - 1) (n - 2) (n - 3)}