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# scipy.stats.ppcc_plot

scipy.stats.ppcc_plot(x, a, b, dist='tukeylambda', plot=None, N=80)

  Calculate and optionally plot probability plot correlation coefficient.

  The probability plot correlation coefficient (PPCC) plot can be used to determine the optimal shape parameter for a one-parameter family of distributions. It cannot be used for distributions without shape parameters (like the normal distribution) or with multiple shape parameters.

  By default a Tukey-Lambda distribution (stats.tukeylambda) is used. A Tukey-Lambda PPCC plot interpolates from long-tailed to short-tailed distributions via an approximately normal one, and is therefore particularly useful in practice.

  Parameters:
    x array_like

      Input array.

    a, b scalar

      Lower and upper bounds of the shape parameter to use.

    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'`.

    plot object, optional

      If given, plots PPCC against the shape parameter. plot is an object that has to have methods “plot” and “text”. The `matplotlib.pyplot` module or a Matplotlib Axes object can be used, or a custom object with the same methods. Default is None, which means that no plot is created.

    N int, optional

      Number of points on the horizontal axis (equally distributed from a to b).

  Returns:
    svals ndarray

      The shape values for which ppcc was calculated.

    ppcc ndarray

      The calculated probability plot correlation coefficient values.

  See also

  `ppcc_max`, `probplot`, `boxcox_normplot`, `tukeylambda`

  References

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

  Examples

  First we generate some random data from a Weibull distribution with shape parameter 2.5, and plot the histogram of the data:

      >>> import numpy as np
      >>> 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)

  Take a look at the histogram of the data.

      >>> fig1, ax = plt.subplots(figsize=(9, 4))
      >>> ax.hist(x, bins=50)
      >>> ax.set_title('Histogram of x')
      >>> plt.show()

  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 `c` used above):

      >>> fig2 = plt.figure(figsize=(12, 4))
      >>> ax1 = fig2.add_subplot(1, 3, 1)
      >>> ax2 = fig2.add_subplot(1, 3, 2)
      >>> ax3 = fig2.add_subplot(1, 3, 3)
      >>> res = stats.probplot(x, plot=ax1)
      >>> res = stats.boxcox_normplot(x, -4, 4, plot=ax2)
      >>> res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', plot=ax3)
      >>> ax3.axvline(c, color='r')
      >>> plt.show()