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Module « scipy.stats »

Fonction epps_singleton_2samp - module scipy.stats

Signature de la fonction epps_singleton_2samp

def epps_singleton_2samp(x, y, t=(0.4, 0.8), *, axis=0, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.epps_singleton_2samp)

    


Compute the Epps-Singleton (ES) test statistic.

Test the null hypothesis that two samples have the same underlying
probability distribution.

Parameters
----------
x, y : array-like
    The two samples of observations to be tested. Input must not have more
    than one dimension. Samples can have different lengths, but both
    must have at least five observations.
t : array-like, optional
    The points (t1, ..., tn) where the empirical characteristic function is
    to be evaluated. It should be positive distinct numbers. The default
    value (0.4, 0.8) is proposed in [1]_. Input must not have more than
    one dimension.
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
-------
statistic : float
    The test statistic.
pvalue : float
    The associated p-value based on the asymptotic chi2-distribution.

See Also
--------

:func:`ks_2samp`, :func:`anderson_ksamp`
    ..

Notes
-----
Testing whether two samples are generated by the same underlying
distribution is a classical question in statistics. A widely used test is
the Kolmogorov-Smirnov (KS) test which relies on the empirical
distribution function. Epps and Singleton introduce a test based on the
empirical characteristic function in [1]_.

One advantage of the ES test compared to the KS test is that is does
not assume a continuous distribution. In [1]_, the authors conclude
that the test also has a higher power than the KS test in many
examples. They recommend the use of the ES test for discrete samples as
well as continuous samples with at least 25 observations each, whereas
`anderson_ksamp` is recommended for smaller sample sizes in the
continuous case.

The p-value is computed from the asymptotic distribution of the test
statistic which follows a `chi2` distribution. If the sample size of both
`x` and `y` is below 25, the small sample correction proposed in [1]_ is
applied to the test statistic.

The default values of `t` are determined in [1]_ by considering
various distributions and finding good values that lead to a high power
of the test in general. Table III in [1]_ gives the optimal values for
the distributions tested in that study. The values of `t` are scaled by
the semi-interquartile range in the implementation, see [1]_.

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] T. W. Epps and K. J. Singleton, "An omnibus test for the two-sample
   problem using the empirical characteristic function", Journal of
   Statistical Computation and Simulation 26, p. 177--203, 1986.

.. [2] S. J. Goerg and J. Kaiser, "Nonparametric testing of distributions
   - the Epps-Singleton two-sample test using the empirical characteristic
   function", The Stata Journal 9(3), p. 454--465, 2009.

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