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Fonction ppcc_max - module scipy.stats

Signature de la fonction ppcc_max

def ppcc_max(x, brack=(0.0, 1.0), dist='tukeylambda') 

Description

ppcc_max.__doc__

Calculate the shape parameter that maximizes the PPCC.

    The probability plot correlation coefficient (PPCC) plot can be used
    to determine the optimal shape parameter for a one-parameter family
    of distributions. ``ppcc_max`` returns the shape parameter that would
    maximize the probability plot correlation coefficient for the given
    data to a one-parameter family of distributions.

    Parameters
    ----------
    x : array_like
        Input array.
    brack : tuple, optional
        Triple (a,b,c) where (a<b<c). If bracket consists of two numbers (a, c)
        then they are assumed to be a starting interval for a downhill bracket
        search (see `scipy.optimize.brent`).
    dist : str or stats.distributions instance, optional
        Distribution or distribution function name.  Objects that look enough
        like a stats.distributions instance (i.e. they have a ``ppf`` method)
        are also accepted.  The default is ``'tukeylambda'``.

    Returns
    -------
    shape_value : float
        The shape parameter at which the probability plot correlation
        coefficient reaches its max value.

    See Also
    --------
    ppcc_plot, probplot, boxcox

    Notes
    -----
    The brack keyword serves as a starting point which is useful in corner
    cases. One can use a plot to obtain a rough visual estimate of the location
    for the maximum to start the search near it.

    References
    ----------
    .. [1] J.J. Filliben, "The Probability Plot Correlation Coefficient Test
           for Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
    .. [2] Engineering Statistics Handbook, NIST/SEMATEC,
           https://www.itl.nist.gov/div898/handbook/eda/section3/ppccplot.htm

    Examples
    --------
    First we generate some random data from a Weibull distribution
    with shape parameter 2.5:

    >>> from scipy import stats
    >>> import matplotlib.pyplot as plt
    >>> rng = np.random.default_rng()
    >>> c = 2.5
    >>> x = stats.weibull_min.rvs(c, scale=4, size=2000, random_state=rng)

    Generate the PPCC plot for this data with the Weibull distribution.

    >>> fig, ax = plt.subplots(figsize=(8, 6))
    >>> res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', plot=ax)

    We calculate the value where the shape should reach its maximum and a
    red line is drawn there. The line should coincide with the highest
    point in the PPCC graph.

    >>> cmax = stats.ppcc_max(x, brack=(c/2, 2*c), dist='weibull_min')
    >>> ax.axvline(cmax, color='r')
    >>> plt.show()