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Fonction cramervonmises - module scipy.stats

Signature de la fonction cramervonmises

def cramervonmises(rvs, cdf, args=()) 

Description

cramervonmises.__doc__

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`.
    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.

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

    See Also
    --------
    kstest, 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.

    References
    ----------
    .. [1] Cramér-von Mises criterion, Wikipedia,
           https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93von_Mises_criterion
    .. [2] Csorgo, 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.

    >>> from scipy import stats
    >>> rng = np.random.default_rng()
    >>> x = stats.norm.rvs(size=500, random_state=rng)
    >>> res = stats.cramervonmises(x, 'norm')
    >>> res.statistic, res.pvalue
    (0.49121480855028343, 0.04189256516661377)

    The p-value 0.79 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
    (0.07400330012187435, 0.7274595666160468)

    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
    (0.07400330012187435, 0.7274595666160468)

    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 0.04 is less than our chosen
    significance level.