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Fonction kstest - module scipy.stats

Signature de la fonction kstest

def kstest(rvs, cdf, args=(), N=20, alternative='two-sided', mode='auto') 

Description

kstest.__doc__

    Performs the (one-sample or two-sample) Kolmogorov-Smirnov test for
    goodness of fit.

    The one-sample test compares the underlying distribution F(x) of a sample
    against a given distribution G(x). The two-sample test compares the
    underlying distributions of two independent samples. Both tests are valid
    only for continuous distributions.

    Parameters
    ----------
    rvs : str, array_like, or callable
        If an array, it should be a 1-D array of observations of random
        variables.
        If a callable, it should be a function to generate random variables;
        it is required to have a keyword argument `size`.
        If a string, it should be the name of a distribution in `scipy.stats`,
        which will be used to generate random variables.
    cdf : str, array_like or callable
        If array_like, it should be a 1-D array of observations of random
        variables, and the two-sample test is performed
        (and rvs must be array_like).
        If a callable, that callable is used to calculate the cdf.
        If a string, it should be the name of a distribution in `scipy.stats`,
        which will be used as the cdf function.
    args : tuple, sequence, optional
        Distribution parameters, used if `rvs` or `cdf` are strings or
        callables.
    N : int, optional
        Sample size if `rvs` is string or callable.  Default is 20.
    alternative : {'two-sided', 'less', 'greater'}, optional
        Defines the null and alternative hypotheses. Default is 'two-sided'.
        Please see explanations in the Notes below.
    mode : {'auto', 'exact', 'approx', 'asymp'}, optional
        Defines the distribution used for calculating the p-value.
        The following options are available (default is 'auto'):

          * 'auto' : selects one of the other options.
          * 'exact' : uses the exact distribution of test statistic.
          * 'approx' : approximates the two-sided probability with twice the
            one-sided probability
          * 'asymp': uses asymptotic distribution of test statistic

    Returns
    -------
    statistic : float
        KS test statistic, either D, D+ or D-.
    pvalue :  float
        One-tailed or two-tailed p-value.

    See Also
    --------
    ks_2samp

    Notes
    -----
    There are three options for the null and corresponding alternative
    hypothesis that can be selected using the `alternative` parameter.

    - `two-sided`: The null hypothesis is that the two distributions are
      identical, F(x)=G(x) for all x; the alternative is that they are not
      identical.

    - `less`: The null hypothesis is that F(x) >= G(x) for all x; the
      alternative is that F(x) < G(x) for at least one x.

    - `greater`: The null hypothesis is that F(x) <= G(x) for all x; the
      alternative is that F(x) > G(x) for at least one x.

    Note that the alternative hypotheses describe the *CDFs* of the
    underlying distributions, not the observed values. For example,
    suppose x1 ~ F and x2 ~ G. If F(x) > G(x) for all x, the values in
    x1 tend to be less than those in x2.


    Examples
    --------
    >>> from scipy import stats
    >>> rng = np.random.default_rng()

    >>> x = np.linspace(-15, 15, 9)
    >>> stats.kstest(x, 'norm')
    KstestResult(statistic=0.444356027159..., pvalue=0.038850140086...)

    >>> stats.kstest(stats.norm.rvs(size=100, random_state=rng), stats.norm.cdf)
    KstestResult(statistic=0.165471391799..., pvalue=0.007331283245...)

    The above lines are equivalent to:

    >>> stats.kstest(stats.norm.rvs, 'norm', N=100)
    KstestResult(statistic=0.113810164200..., pvalue=0.138690052319...)  # may vary

    *Test against one-sided alternative hypothesis*

    Shift distribution to larger values, so that ``CDF(x) < norm.cdf(x)``:

    >>> x = stats.norm.rvs(loc=0.2, size=100, random_state=rng)
    >>> stats.kstest(x, 'norm', alternative='less')
    KstestResult(statistic=0.1002033514..., pvalue=0.1255446444...)

    Reject null hypothesis in favor of alternative hypothesis: less

    >>> stats.kstest(x, 'norm', alternative='greater')
    KstestResult(statistic=0.018749806388..., pvalue=0.920581859791...)

    Don't reject null hypothesis in favor of alternative hypothesis: greater

    >>> stats.kstest(x, 'norm')
    KstestResult(statistic=0.100203351482..., pvalue=0.250616879765...)

    *Testing t distributed random variables against normal distribution*

    With 100 degrees of freedom the t distribution looks close to the normal
    distribution, and the K-S test does not reject the hypothesis that the
    sample came from the normal distribution:

    >>> stats.kstest(stats.t.rvs(100, size=100, random_state=rng), 'norm')
    KstestResult(statistic=0.064273776544..., pvalue=0.778737758305...)

    With 3 degrees of freedom the t distribution looks sufficiently different
    from the normal distribution, that we can reject the hypothesis that the
    sample came from the normal distribution at the 10% level:

    >>> stats.kstest(stats.t.rvs(3, size=100, random_state=rng), 'norm')
    KstestResult(statistic=0.128678487493..., pvalue=0.066569081515...)