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 Tukey-Lambda distribution, with shape parameter -0.7:

>>> from scipy import stats
>>> import matplotlib.pyplot as plt
>>> np.random.seed(1234567)
>>> x = stats.tukeylambda.rvs(-0.7, loc=2, scale=0.5, size=10000) + 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):

>>> fig = plt.figure(figsize=(12, 4))
>>> ax1 = fig.add_subplot(131)
>>> ax2 = fig.add_subplot(132)
>>> ax3 = fig.add_subplot(133)
>>> res = stats.probplot(x, plot=ax1)
>>> res = stats.boxcox_normplot(x, -5, 5, plot=ax2)
>>> res = stats.ppcc_plot(x, -5, 5, plot=ax3)
>>> ax3.vlines(-0.7, 0, 1, colors='r', label='Expected shape value')
>>> plt.show()