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Module « scipy.stats »

Fonction probplot - module scipy.stats

Signature de la fonction probplot

def probplot(x, sparams=(), dist='norm', fit=True, plot=None, rvalue=False) 

Description

help(scipy.stats.probplot)

Calculate quantiles for a probability plot, and optionally show the plot.

Generates a probability plot of sample data against the quantiles of a
specified theoretical distribution (the normal distribution by default).
`probplot` optionally calculates a best-fit line for the data and plots the
results using Matplotlib or a given plot function.

Parameters
----------
x : array_like
    Sample/response data from which `probplot` creates the plot.
sparams : tuple, optional
    Distribution-specific shape parameters (shape parameters plus location
    and scale).
dist : str or stats.distributions instance, optional
    Distribution or distribution function name. The default is 'norm' for a
    normal probability plot.  Objects that look enough like a
    stats.distributions instance (i.e. they have a ``ppf`` method) are also
    accepted.
fit : bool, optional
    Fit a least-squares regression (best-fit) line to the sample data if
    True (default).
plot : object, optional
    If given, plots the quantiles.
    If given and `fit` is True, also plots the least squares fit.
    `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.
rvalue : bool, optional
    If `plot` is provided and `fit` is True, setting `rvalue` to True
    includes the coefficient of determination on the plot.
    Default is False.

Returns
-------
(osm, osr) : tuple of ndarrays
    Tuple of theoretical quantiles (osm, or order statistic medians) and
    ordered responses (osr).  `osr` is simply sorted input `x`.
    For details on how `osm` is calculated see the Notes section.
(slope, intercept, r) : tuple of floats, optional
    Tuple  containing the result of the least-squares fit, if that is
    performed by `probplot`. `r` is the square root of the coefficient of
    determination.  If ``fit=False`` and ``plot=None``, this tuple is not
    returned.

Notes
-----
Even if `plot` is given, the figure is not shown or saved by `probplot`;
``plt.show()`` or ``plt.savefig('figname.png')`` should be used after
calling `probplot`.

`probplot` generates a probability plot, which should not be confused with
a Q-Q or a P-P plot.  Statsmodels has more extensive functionality of this
type, see ``statsmodels.api.ProbPlot``.

The formula used for the theoretical quantiles (horizontal axis of the
probability plot) is Filliben's estimate::

    quantiles = dist.ppf(val), for

            0.5**(1/n),                  for i = n
      val = (i - 0.3175) / (n + 0.365),  for i = 2, ..., n-1
            1 - 0.5**(1/n),              for i = 1

where ``i`` indicates the i-th ordered value and ``n`` is the total number
of values.

Examples
--------
>>> import numpy as np
>>> from scipy import stats
>>> import matplotlib.pyplot as plt
>>> nsample = 100
>>> rng = np.random.default_rng()

A t distribution with small degrees of freedom:

>>> ax1 = plt.subplot(221)
>>> x = stats.t.rvs(3, size=nsample, random_state=rng)
>>> res = stats.probplot(x, plot=plt)

A t distribution with larger degrees of freedom:

>>> ax2 = plt.subplot(222)
>>> x = stats.t.rvs(25, size=nsample, random_state=rng)
>>> res = stats.probplot(x, plot=plt)

A mixture of two normal distributions with broadcasting:

>>> ax3 = plt.subplot(223)
>>> x = stats.norm.rvs(loc=[0,5], scale=[1,1.5],
...                    size=(nsample//2,2), random_state=rng).ravel()
>>> res = stats.probplot(x, plot=plt)

A standard normal distribution:

>>> ax4 = plt.subplot(224)
>>> x = stats.norm.rvs(loc=0, scale=1, size=nsample, random_state=rng)
>>> res = stats.probplot(x, plot=plt)

Produce a new figure with a loggamma distribution, using the ``dist`` and
``sparams`` keywords:

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> x = stats.loggamma.rvs(c=2.5, size=500, random_state=rng)
>>> res = stats.probplot(x, dist=stats.loggamma, sparams=(2.5,), plot=ax)
>>> ax.set_title("Probplot for loggamma dist with shape parameter 2.5")

Show the results with Matplotlib:

>>> plt.show()

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