- 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.
- a, bscalar
Lower and upper bounds of the shape parameter to use.
- diststr or stats.distributions instance, optional
Distribution or distribution function name. Objects that look enough like a stats.distributions instance (i.e. they have a
ppfmethod) are also accepted. The default is
- plotobject, optional
If given, plots PPCC against the shape parameter. plot is an object that has to have methods “plot” and “text”. The
matplotlib.pyplotmodule 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.
- Nint, optional
Number of points on the horizontal axis (equally distributed from a to b).
The shape values for which ppcc was calculated.
The calculated probability plot correlation coefficient values.
J.J. Filliben, “The Probability Plot Correlation Coefficient Test for Normality”, Technometrics, Vol. 17, pp. 111-117, 1975.
First we generate some random data from a Weibull distribution with shape parameter 2.5, and plot the histogram of the data:
>>> 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
>>> 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()