`scipy.stats._morestats:ppcc_plot`

source: /scipy/stats/_morestats.py :772

Signature

   def     ppcc_plot (    x    ,    a    ,    b    ,    dist    =  tukeylambda   ,    plot    =  None   ,    N    =  80     )

Summary

Calculate and optionally plot probability plot correlation coefficient.

Extended Summary

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.

Notes

Array API Standard Support

ppcc_plot has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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()

✓

Aliases

scipy.stats.ppcc_plot