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Module « scipy.stats »

Fonction ppcc_plot - module scipy.stats

Signature de la fonction ppcc_plot

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

Description

help(scipy.stats.ppcc_plot)

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()

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