Module « scipy.stats »

Fonction boxcox_llf - module scipy.stats

Signature de la fonction boxcox_llf

def boxcox_llf(lmb, data) 

Description

boxcox_llf.__doc__

The boxcox log-likelihood function.

    Parameters
    ----------
    lmb : scalar
        Parameter for Box-Cox transformation.  See `boxcox` for details.
    data : array_like
        Data to calculate Box-Cox log-likelihood for.  If `data` is
        multi-dimensional, the log-likelihood is calculated along the first
        axis.

    Returns
    -------
    llf : float or ndarray
        Box-Cox log-likelihood of `data` given `lmb`.  A float for 1-D `data`,
        an array otherwise.

    See Also
    --------
    boxcox, probplot, boxcox_normplot, boxcox_normmax

    Notes
    -----
    The Box-Cox log-likelihood function is defined here as

    .. math::

        llf = (\lambda - 1) \sum_i(\log(x_i)) -
              N/2 \log(\sum_i (y_i - \bar{y})^2 / N),

    where ``y`` is the Box-Cox transformed input data ``x``.

    Examples
    --------
    >>> from scipy import stats
    >>> import matplotlib.pyplot as plt
    >>> from mpl_toolkits.axes_grid1.inset_locator import inset_axes

    Generate some random variates and calculate Box-Cox log-likelihood values
    for them for a range of ``lmbda`` values:

    >>> rng = np.random.default_rng()
    >>> x = stats.loggamma.rvs(5, loc=10, size=1000, random_state=rng)
    >>> lmbdas = np.linspace(-2, 10)
    >>> llf = np.zeros(lmbdas.shape, dtype=float)
    >>> for ii, lmbda in enumerate(lmbdas):
    ...     llf[ii] = stats.boxcox_llf(lmbda, x)

    Also find the optimal lmbda value with `boxcox`:

    >>> x_most_normal, lmbda_optimal = stats.boxcox(x)

    Plot the log-likelihood as function of lmbda.  Add the optimal lmbda as a
    horizontal line to check that that's really the optimum:

    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(111)
    >>> ax.plot(lmbdas, llf, 'b.-')
    >>> ax.axhline(stats.boxcox_llf(lmbda_optimal, x), color='r')
    >>> ax.set_xlabel('lmbda parameter')
    >>> ax.set_ylabel('Box-Cox log-likelihood')

    Now add some probability plots to show that where the log-likelihood is
    maximized the data transformed with `boxcox` looks closest to normal:

    >>> locs = [3, 10, 4]  # 'lower left', 'center', 'lower right'
    >>> for lmbda, loc in zip([-1, lmbda_optimal, 9], locs):
    ...     xt = stats.boxcox(x, lmbda=lmbda)
    ...     (osm, osr), (slope, intercept, r_sq) = stats.probplot(xt)
    ...     ax_inset = inset_axes(ax, width="20%", height="20%", loc=loc)
    ...     ax_inset.plot(osm, osr, 'c.', osm, slope*osm + intercept, 'k-')
    ...     ax_inset.set_xticklabels([])
    ...     ax_inset.set_yticklabels([])
    ...     ax_inset.set_title(r'$\lambda=%1.2f$' % lmbda)

    >>> plt.show()