Module « scipy.stats »

Classe « gaussian_kde »

Informations générales

Héritage

builtins.object
    gaussian_kde

Définition

class gaussian_kde(builtins.object):

Description _{[extrait de gaussian_kde.__doc__]}

Representation of a kernel-density estimate using Gaussian kernels.

    Kernel density estimation is a way to estimate the probability density
    function (PDF) of a random variable in a non-parametric way.
    `gaussian_kde` works for both uni-variate and multi-variate data.   It
    includes automatic bandwidth determination.  The estimation works best for
    a unimodal distribution; bimodal or multi-modal distributions tend to be
    oversmoothed.

    Parameters
    ----------
    dataset : array_like
        Datapoints to estimate from. In case of univariate data this is a 1-D
        array, otherwise a 2-D array with shape (# of dims, # of data).
    bw_method : str, scalar or callable, optional
        The method used to calculate the estimator bandwidth.  This can be
        'scott', 'silverman', a scalar constant or a callable.  If a scalar,
        this will be used directly as `kde.factor`.  If a callable, it should
        take a `gaussian_kde` instance as only parameter and return a scalar.
        If None (default), 'scott' is used.  See Notes for more details.
    weights : array_like, optional
        weights of datapoints. This must be the same shape as dataset.
        If None (default), the samples are assumed to be equally weighted

    Attributes
    ----------
    dataset : ndarray
        The dataset with which `gaussian_kde` was initialized.
    d : int
        Number of dimensions.
    n : int
        Number of datapoints.
    neff : int
        Effective number of datapoints.

        .. versionadded:: 1.2.0
    factor : float
        The bandwidth factor, obtained from `kde.covariance_factor`, with which
        the covariance matrix is multiplied.
    covariance : ndarray
        The covariance matrix of `dataset`, scaled by the calculated bandwidth
        (`kde.factor`).
    inv_cov : ndarray
        The inverse of `covariance`.

    Methods
    -------
    evaluate
    __call__
    integrate_gaussian
    integrate_box_1d
    integrate_box
    integrate_kde
    pdf
    logpdf
    resample
    set_bandwidth
    covariance_factor

    Notes
    -----
    Bandwidth selection strongly influences the estimate obtained from the KDE
    (much more so than the actual shape of the kernel).  Bandwidth selection
    can be done by a "rule of thumb", by cross-validation, by "plug-in
    methods" or by other means; see [3]_, [4]_ for reviews.  `gaussian_kde`
    uses a rule of thumb, the default is Scott's Rule.

    Scott's Rule [1]_, implemented as `scotts_factor`, is::

        n**(-1./(d+4)),

    with ``n`` the number of data points and ``d`` the number of dimensions.
    In the case of unequally weighted points, `scotts_factor` becomes::

        neff**(-1./(d+4)),

    with ``neff`` the effective number of datapoints.
    Silverman's Rule [2]_, implemented as `silverman_factor`, is::

        (n * (d + 2) / 4.)**(-1. / (d + 4)).

    or in the case of unequally weighted points::

        (neff * (d + 2) / 4.)**(-1. / (d + 4)).

    Good general descriptions of kernel density estimation can be found in [1]_
    and [2]_, the mathematics for this multi-dimensional implementation can be
    found in [1]_.

    With a set of weighted samples, the effective number of datapoints ``neff``
    is defined by::

        neff = sum(weights)^2 / sum(weights^2)

    as detailed in [5]_.

    References
    ----------
    .. [1] D.W. Scott, "Multivariate Density Estimation: Theory, Practice, and
           Visualization", John Wiley & Sons, New York, Chicester, 1992.
    .. [2] B.W. Silverman, "Density Estimation for Statistics and Data
           Analysis", Vol. 26, Monographs on Statistics and Applied Probability,
           Chapman and Hall, London, 1986.
    .. [3] B.A. Turlach, "Bandwidth Selection in Kernel Density Estimation: A
           Review", CORE and Institut de Statistique, Vol. 19, pp. 1-33, 1993.
    .. [4] D.M. Bashtannyk and R.J. Hyndman, "Bandwidth selection for kernel
           conditional density estimation", Computational Statistics & Data
           Analysis, Vol. 36, pp. 279-298, 2001.
    .. [5] Gray P. G., 1969, Journal of the Royal Statistical Society.
           Series A (General), 132, 272

    Examples
    --------
    Generate some random two-dimensional data:

    >>> from scipy import stats
    >>> def measure(n):
    ...     "Measurement model, return two coupled measurements."
    ...     m1 = np.random.normal(size=n)
    ...     m2 = np.random.normal(scale=0.5, size=n)
    ...     return m1+m2, m1-m2

    >>> m1, m2 = measure(2000)
    >>> xmin = m1.min()
    >>> xmax = m1.max()
    >>> ymin = m2.min()
    >>> ymax = m2.max()

    Perform a kernel density estimate on the data:

    >>> X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
    >>> positions = np.vstack([X.ravel(), Y.ravel()])
    >>> values = np.vstack([m1, m2])
    >>> kernel = stats.gaussian_kde(values)
    >>> Z = np.reshape(kernel(positions).T, X.shape)

    Plot the results:

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> ax.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,
    ...           extent=[xmin, xmax, ymin, ymax])
    >>> ax.plot(m1, m2, 'k.', markersize=2)
    >>> ax.set_xlim([xmin, xmax])
    >>> ax.set_ylim([ymin, ymax])
    >>> plt.show()

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, dataset, bw_method=None, weights=None)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __init_subclass__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__