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Module « scipy.stats »

Fonction ppcc_max - module scipy.stats

Signature de la fonction ppcc_max

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

Description

help(scipy.stats.ppcc_max)

Calculate the shape parameter that maximizes the PPCC.

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.

See Also
--------
ppcc_plot, probplot, boxcox

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.

References
----------
.. [1] J.J. Filliben, "The Probability Plot Correlation Coefficient Test
       for Normality", Technometrics, Vol. 17, pp. 111-117, 1975.
.. [2] Engineering Statistics Handbook, NIST/SEMATEC,
       https://www.itl.nist.gov/div898/handbook/eda/section3/ppccplot.htm

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()

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