`scipy.stats._morestats:ppcc_max`

source: /scipy/stats/_morestats.py :683

Signature

def ppcc_max ( x , brack = (0.0, 1.0) , dist = tukeylambda )

Summary

Calculate the shape parameter that maximizes the PPCC.

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. 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.

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.

Array API Standard Support

ppcc_max 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:

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)

✓

Generate the PPCC plot for this data with the Weibull distribution.

fig, ax = plt.subplots(figsize=(8, 6))
res = stats.ppcc_plot(x, c/2, 2*c, dist='weibull_min', 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 graph.

cmax = stats.ppcc_max(x, brack=(c/2, 2*c), dist='weibull_min')

✓

ax.axvline(cmax, color='r')

✗

plt.show()

✓

Aliases

scipy.stats.ppcc_max