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# scipy.stats.ppcc_max

`scipy.stats.``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

  [R599] | J.J. Filliben, “The Probability Plot Correlation Coefficient Test for Normality”, Technometrics, Vol. 17, pp. 111-117, 1975.

  [R600] | http://www.itl.nist.gov/div898/handbook/eda/section3/ppccplot.htm

  Examples

  First we generate some random data from a Tukey-Lambda distribution, with shape parameter -0.7:

      >>> from scipy import stats
      >>> x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000,
      ...                           random_state=1234567) + 1e4

  Now we explore this data with a PPCC plot as well as the related probability plot and Box-Cox normplot. A red line is drawn where we expect the PPCC value to be maximal (at the shape parameter -0.7 used above):

      >>> import matplotlib.pyplot as plt
      >>> fig = plt.figure(figsize=(8, 6))
      >>> ax = fig.add_subplot(111)
      >>> res = stats.ppcc_plot(x, -5, 5, 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_plot.

      >>> max = stats.ppcc_max(x)
      >>> ax.vlines(max, 0, 1, colors='r', label='Expected shape value')

      >>> plt.show()

  (Source code)