Module « scipy.stats »

Fonction kstwo - module scipy.stats

Signature de la fonction kstwo

def kstwo(*args, **kwds) 

Description

kstwo.__doc__

Kolmogorov-Smirnov two-sided test statistic distribution.

    This is the distribution of the two-sided Kolmogorov-Smirnov (KS)
    statistic :math:`D_n` for a finite sample size ``n``
    (the shape parameter).

    As an instance of the `rv_continuous` class, `kstwo` object inherits from it
    a collection of generic methods (see below for the full list),
    and completes them with details specific for this particular distribution.
    
    Methods
    -------
    rvs(n, loc=0, scale=1, size=1, random_state=None)
        Random variates.
    pdf(x, n, loc=0, scale=1)
        Probability density function.
    logpdf(x, n, loc=0, scale=1)
        Log of the probability density function.
    cdf(x, n, loc=0, scale=1)
        Cumulative distribution function.
    logcdf(x, n, loc=0, scale=1)
        Log of the cumulative distribution function.
    sf(x, n, loc=0, scale=1)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(x, n, loc=0, scale=1)
        Log of the survival function.
    ppf(q, n, loc=0, scale=1)
        Percent point function (inverse of ``cdf`` --- percentiles).
    isf(q, n, loc=0, scale=1)
        Inverse survival function (inverse of ``sf``).
    moment(n, n, loc=0, scale=1)
        Non-central moment of order n
    stats(n, loc=0, scale=1, moments='mv')
        Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
    entropy(n, loc=0, scale=1)
        (Differential) entropy of the RV.
    fit(data)
        Parameter estimates for generic data.
        See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
        keyword arguments.
    expect(func, args=(n,), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
        Expected value of a function (of one argument) with respect to the distribution.
    median(n, loc=0, scale=1)
        Median of the distribution.
    mean(n, loc=0, scale=1)
        Mean of the distribution.
    var(n, loc=0, scale=1)
        Variance of the distribution.
    std(n, loc=0, scale=1)
        Standard deviation of the distribution.
    interval(alpha, n, loc=0, scale=1)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

    See Also
    --------
    kstwobign, ksone, kstest

    Notes
    -----
    :math:`D_n` is given by

    .. math::

        D_n = \text{sup}_x |F_n(x) - F(x)|

    where :math:`F` is a (continuous) CDF and :math:`F_n` is an empirical CDF.
    `kstwo` describes the distribution under the null hypothesis of the KS test
    that the empirical CDF corresponds to :math:`n` i.i.d. random variates
    with CDF :math:`F`.

    The probability density above is defined in the "standardized" form. To shift
    and/or scale the distribution use the ``loc`` and ``scale`` parameters.
    Specifically, ``kstwo.pdf(x, n, loc, scale)`` is identically
    equivalent to ``kstwo.pdf(y, n) / scale`` with
    ``y = (x - loc) / scale``. Note that shifting the location of a distribution
    does not make it a "noncentral" distribution; noncentral generalizations of
    some distributions are available in separate classes.

    References
    ----------
    .. [1] Simard, R., L'Ecuyer, P. "Computing the Two-Sided
       Kolmogorov-Smirnov Distribution",  Journal of Statistical Software,
       Vol 39, 11, 1-18 (2011).

    Examples
    --------
    >>> from scipy.stats import kstwo
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> n = 10
    >>> mean, var, skew, kurt = kstwo.stats(n, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(kstwo.ppf(0.01, n),
    ...                 kstwo.ppf(0.99, n), 100)
    >>> ax.plot(x, kstwo.pdf(x, n),
    ...        'r-', lw=5, alpha=0.6, label='kstwo pdf')
    
    Alternatively, the distribution object can be called (as a function)
    to fix the shape, location and scale parameters. This returns a "frozen"
    RV object holding the given parameters fixed.
    
    Freeze the distribution and display the frozen ``pdf``:
    
    >>> rv = kstwo(n)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = kstwo.ppf([0.001, 0.5, 0.999], n)
    >>> np.allclose([0.001, 0.5, 0.999], kstwo.cdf(vals, n))
    True
    
    Generate random numbers:
    
    >>> r = kstwo.rvs(n, size=1000)
    
    And compare the histogram:
    
    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()