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Fonction kurtosis - module scipy.stats

Signature de la fonction kurtosis

def kurtosis(a, axis=0, fisher=True, bias=True, nan_policy='propagate') 

Description

kurtosis.__doc__

Compute the kurtosis (Fisher or Pearson) of a dataset.

    Kurtosis is the fourth central moment divided by the square of the
    variance. If Fisher's definition is used, then 3.0 is subtracted from
    the result to give 0.0 for a normal distribution.

    If bias is False then the kurtosis is calculated using k statistics to
    eliminate bias coming from biased moment estimators

    Use `kurtosistest` to see if result is close enough to normal.

    Parameters
    ----------
    a : array
        Data for which the kurtosis is calculated.
    axis : int or None, optional
        Axis along which the kurtosis is calculated. Default is 0.
        If None, compute over the whole array `a`.
    fisher : bool, optional
        If True, Fisher's definition is used (normal ==> 0.0). If False,
        Pearson's definition is used (normal ==> 3.0).
    bias : bool, optional
        If False, then the calculations are corrected for statistical bias.
    nan_policy : {'propagate', 'raise', 'omit'}, optional
        Defines how to handle when input contains nan. 'propagate' returns nan,
        'raise' throws an error, 'omit' performs the calculations ignoring nan
        values. Default is 'propagate'.

    Returns
    -------
    kurtosis : array
        The kurtosis of values along an axis. If all values are equal,
        return -3 for Fisher's definition and 0 for Pearson's definition.

    References
    ----------
    .. [1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard
       Probability and Statistics Tables and Formulae. Chapman & Hall: New
       York. 2000.

    Examples
    --------
    In Fisher's definiton, the kurtosis of the normal distribution is zero.
    In the following example, the kurtosis is close to zero, because it was
    calculated from the dataset, not from the continuous distribution.

    >>> from scipy.stats import norm, kurtosis
    >>> data = norm.rvs(size=1000, random_state=3)
    >>> kurtosis(data)
    -0.06928694200380558

    The distribution with a higher kurtosis has a heavier tail.
    The zero valued kurtosis of the normal distribution in Fisher's definition
    can serve as a reference point.

    >>> import matplotlib.pyplot as plt
    >>> import scipy.stats as stats
    >>> from scipy.stats import kurtosis

    >>> x = np.linspace(-5, 5, 100)
    >>> ax = plt.subplot()
    >>> distnames = ['laplace', 'norm', 'uniform']

    >>> for distname in distnames:
    ...     if distname == 'uniform':
    ...         dist = getattr(stats, distname)(loc=-2, scale=4)
    ...     else:
    ...         dist = getattr(stats, distname)
    ...     data = dist.rvs(size=1000)
    ...     kur = kurtosis(data, fisher=True)
    ...     y = dist.pdf(x)
    ...     ax.plot(x, y, label="{}, {}".format(distname, round(kur, 3)))
    ...     ax.legend()

    The Laplace distribution has a heavier tail than the normal distribution.
    The uniform distribution (which has negative kurtosis) has the thinnest
    tail.