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Module « scipy.stats »

Fonction cramervonmises - module scipy.stats

Signature de la fonction cramervonmises

def cramervonmises(rvs, cdf, args=(), *, axis=0, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.cramervonmises)

    


Perform the one-sample Cramér-von Mises test for goodness of fit.

This performs a test of the goodness of fit of a cumulative distribution
function (cdf) :math:`F` compared to the empirical distribution function
:math:`F_n` of observed random variates :math:`X_1, ..., X_n` that are
assumed to be independent and identically distributed ([1]_).
The null hypothesis is that the :math:`X_i` have cumulative distribution
:math:`F`.

Parameters
----------
rvs : array_like
    A 1-D array of observed values of the random variables :math:`X_i`.
    The sample must contain at least two observations.
cdf : str or callable
    The cumulative distribution function :math:`F` to test the
    observations against. If a string, it should be the name of a
    distribution in `scipy.stats`. If a callable, that callable is used
    to calculate the cdf: ``cdf(x, *args) -> float``.
args : tuple, optional
    Distribution parameters. These are assumed to be known; see Notes.
axis : int or None, default: 0
    If an int, the axis of the input along which to compute the statistic.
    The statistic of each axis-slice (e.g. row) of the input will appear in a
    corresponding element of the output.
    If ``None``, the input will be raveled before computing the statistic.
nan_policy : {'propagate', 'omit', 'raise'}
    Defines how to handle input NaNs.
    
    - ``propagate``: if a NaN is present in the axis slice (e.g. row) along
      which the  statistic is computed, the corresponding entry of the output
      will be NaN.
    - ``omit``: NaNs will be omitted when performing the calculation.
      If insufficient data remains in the axis slice along which the
      statistic is computed, the corresponding entry of the output will be
      NaN.
    - ``raise``: if a NaN is present, a ``ValueError`` will be raised.
keepdims : bool, default: False
    If this is set to True, the axes which are reduced are left
    in the result as dimensions with size one. With this option,
    the result will broadcast correctly against the input array.

Returns
-------
res : object with attributes
    statistic : float
        Cramér-von Mises statistic.
    pvalue : float
        The p-value.

See Also
--------

:func:`kstest`, :func:`cramervonmises_2samp`
    ..

Notes
-----
.. versionadded:: 1.6.0

The p-value relies on the approximation given by equation 1.8 in [2]_.
It is important to keep in mind that the p-value is only accurate if
one tests a simple hypothesis, i.e. the parameters of the reference
distribution are known. If the parameters are estimated from the data
(composite hypothesis), the computed p-value is not reliable.

Beginning in SciPy 1.9, ``np.matrix`` inputs (not recommended for new
code) are converted to ``np.ndarray`` before the calculation is performed. In
this case, the output will be a scalar or ``np.ndarray`` of appropriate shape
rather than a 2D ``np.matrix``. Similarly, while masked elements of masked
arrays are ignored, the output will be a scalar or ``np.ndarray`` rather than a
masked array with ``mask=False``.

References
----------
.. [1] Cramér-von Mises criterion, Wikipedia,
       https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion
.. [2] Csörgő, S. and Faraway, J. (1996). The Exact and Asymptotic
       Distribution of Cramér-von Mises Statistics. Journal of the
       Royal Statistical Society, pp. 221-234.

Examples
--------
Suppose we wish to test whether data generated by ``scipy.stats.norm.rvs``
were, in fact, drawn from the standard normal distribution. We choose a
significance level of ``alpha=0.05``.

>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng(165417232101553420507139617764912913465)
>>> x = stats.norm.rvs(size=500, random_state=rng)
>>> res = stats.cramervonmises(x, 'norm')
>>> res.statistic, res.pvalue
(0.1072085112565724, 0.5508482238203407)

The p-value exceeds our chosen significance level, so we do not
reject the null hypothesis that the observed sample is drawn from the
standard normal distribution.

Now suppose we wish to check whether the same samples shifted by 2.1 is
consistent with being drawn from a normal distribution with a mean of 2.

>>> y = x + 2.1
>>> res = stats.cramervonmises(y, 'norm', args=(2,))
>>> res.statistic, res.pvalue
(0.8364446265294695, 0.00596286797008283)

Here we have used the `args` keyword to specify the mean (``loc``)
of the normal distribution to test the data against. This is equivalent
to the following, in which we create a frozen normal distribution with
mean 2.1, then pass its ``cdf`` method as an argument.

>>> frozen_dist = stats.norm(loc=2)
>>> res = stats.cramervonmises(y, frozen_dist.cdf)
>>> res.statistic, res.pvalue
(0.8364446265294695, 0.00596286797008283)

In either case, we would reject the null hypothesis that the observed
sample is drawn from a normal distribution with a mean of 2 (and default
variance of 1) because the p-value is less than our chosen
significance level.

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