code: def ppcc_max(x, brack=(0.0, 1.0), dist="tukeylambda"):
      """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()
  
      """
      dist = _parse_dist_kw(dist)
      osm_uniform = _calc_uniform_order_statistic_medians(len(x))
      osr = sort(x)
  
      # this function computes the x-axis values of the probability plot
      #  and computes a linear regression (including the correlation)
      #  and returns 1-r so that a minimization function maximizes the
      #  correlation
      def tempfunc(shape, mi, yvals, func):
          xvals = func(mi, shape)
          r, prob = stats.pearsonr(xvals, yvals)
          return 1 - r
  
      return optimize.brent(
          tempfunc, brack=brack, args=(osm_uniform, osr, dist.ppf)
      )
  
imports: from __future__ import annotations
  import math
  import warnings
  from collections import namedtuple
  import numpy
  from numpy import isscalar, r_, log, around, unique, asarray, zeros, arange, sort, amin, amax, atleast_1d, sqrt, array, compress, pi, exp, ravel, count_nonzero, sin, cos, arctan2, hypot
  from scipy import optimize
  from scipy import special
  from .None import statlib
  from .None import stats
  from .stats import find_repeats, _contains_nan, _normtest_finish
  from .contingency import chi2_contingency
  from .None import distributions
  from ._distn_infrastructure import rv_generic
  from ._hypotests import _get_wilcoxon_distr
label_desc: Use image node_id 9 for calling a global function with example usage: ppcc_max(x, brack, dist) and returns: optimize, unknown