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Fonction boxcox_normmax - module scipy.stats

Signature de la fonction boxcox_normmax

def boxcox_normmax(x, brack=None, method='pearsonr', optimizer=None) 

Description

boxcox_normmax.__doc__

Compute optimal Box-Cox transform parameter for input data.

    Parameters
    ----------
    x : array_like
        Input array.
    brack : 2-tuple, optional, default (-2.0, 2.0)
         The starting interval for a downhill bracket search for the default
         `optimize.brent` solver. Note that this is in most cases not
         critical; the final result is allowed to be outside this bracket.
         If `optimizer` is passed, `brack` must be None.
    method : str, optional
        The method to determine the optimal transform parameter (`boxcox`
        ``lmbda`` parameter). Options are:

        'pearsonr'  (default)
            Maximizes the Pearson correlation coefficient between
            ``y = boxcox(x)`` and the expected values for ``y`` if `x` would be
            normally-distributed.

        'mle'
            Minimizes the log-likelihood `boxcox_llf`.  This is the method used
            in `boxcox`.

        'all'
            Use all optimization methods available, and return all results.
            Useful to compare different methods.
    optimizer : callable, optional
        `optimizer` is a callable that accepts one argument:

        fun : callable
            The objective function to be optimized. `fun` accepts one argument,
            the Box-Cox transform parameter `lmbda`, and returns the negative
            log-likelihood function at the provided value. The job of `optimizer`
            is to find the value of `lmbda` that minimizes `fun`.

        and returns an object, such as an instance of
        `scipy.optimize.OptimizeResult`, which holds the optimal value of
        `lmbda` in an attribute `x`.

        See the example below or the documentation of
        `scipy.optimize.minimize_scalar` for more information.

    Returns
    -------
    maxlog : float or ndarray
        The optimal transform parameter found.  An array instead of a scalar
        for ``method='all'``.

    See Also
    --------
    boxcox, boxcox_llf, boxcox_normplot, scipy.optimize.minimize_scalar

    Examples
    --------
    >>> from scipy import stats
    >>> import matplotlib.pyplot as plt

    We can generate some data and determine the optimal ``lmbda`` in various
    ways:

    >>> rng = np.random.default_rng()
    >>> x = stats.loggamma.rvs(5, size=30, random_state=rng) + 5
    >>> y, lmax_mle = stats.boxcox(x)
    >>> lmax_pearsonr = stats.boxcox_normmax(x)

    >>> lmax_mle
    1.4613865614008015
    >>> lmax_pearsonr
    1.6685004886804342
    >>> stats.boxcox_normmax(x, method='all')
    array([1.66850049, 1.46138656])

    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(111)
    >>> prob = stats.boxcox_normplot(x, -10, 10, plot=ax)
    >>> ax.axvline(lmax_mle, color='r')
    >>> ax.axvline(lmax_pearsonr, color='g', ls='--')

    >>> plt.show()

    Alternatively, we can define our own `optimizer` function. Suppose we
    are only interested in values of `lmbda` on the interval [6, 7], we
    want to use `scipy.optimize.minimize_scalar` with ``method='bounded'``,
    and we want to use tighter tolerances when optimizing the log-likelihood
    function. To do this, we define a function that accepts positional argument
    `fun` and uses `scipy.optimize.minimize_scalar` to minimize `fun` subject
    to the provided bounds and tolerances:

    >>> from scipy import optimize
    >>> options = {'xatol': 1e-12}  # absolute tolerance on `x`
    >>> def optimizer(fun):
    ...     return optimize.minimize_scalar(fun, bounds=(6, 7),
    ...                                     method="bounded", options=options)
    >>> stats.boxcox_normmax(x, optimizer=optimizer)
    6.000...