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Module « scipy.stats »

Fonction kstwo - module scipy.stats

Signature de la fonction kstwo

def kstwo(*args, **kwds) 

Description

help(scipy.stats.kstwo)

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 >= 1``
(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(order, n, loc=0, scale=1)
    Non-central moment of the specified order.
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(confidence, n, loc=0, scale=1)
    Confidence interval with equal areas around the median.

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
--------
>>> import numpy as np
>>> from scipy.stats import kstwo
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Display the probability density function (``pdf``):

>>> n = 10
>>> 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')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

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

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