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https://github.com/wrwrwr/scikit-gof

Variations on goodness of fit tests for SciPy.
https://github.com/wrwrwr/scikit-gof

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Variations on goodness of fit tests for SciPy.

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README 

          
==========

scikit-gof

==========



Provides variants of Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling

goodness of fit tests for fully specified continuous distributions.



Example

=======



.. code:: python



    >>> from scipy.stats import norm, uniform

    >>> from skgof import ks_test, cvm_test, ad_test



    >>> ks_test((1, 2, 3), uniform(0, 4))

    GofResult(statistic=0.25, pvalue=0.97...)



    >>> cvm_test((1, 2, 3), uniform(0, 4))

    GofResult(statistic=0.04..., pvalue=0.95...)



    >>> data = norm(0, 1).rvs(random_state=1, size=100)

    >>> ad_test(data, norm(0, 1))

    GofResult(statistic=0.75..., pvalue=0.51...)

    >>> ad_test(data, norm(.3, 1))

    GofResult(statistic=3.52..., pvalue=0.01...)



Simple tests

============



Scikit-gof currently only offers three nonparametric tests that let you

compare a sample with a reference probability distribution. These are:



``ks_test()``

    Kolmogorov-Smirnov supremum statistic; almost the same as

    ``scipy.stats.kstest()`` with ``alternative='two-sided'`` but with

    (hopefully) somewhat more precise p-value calculation;



``cvm_test()``

    Cramer-von Mises L2 statistic, with a rather crude estimation of the

    statistic distribution (but seemingly the best available);



``ad_test()``

    Anderson-Darling statistic with a fair approximation of its distribution;

    unlike the composite ``scipy.stats.anderson()`` this one needs a fully

    specified hypothesized distribution.



Simple test functions use a common interface, taking as the first argument the

data (sample) to be compared and as the second argument a frozen ``scipy.stats``

distribution.

They return a named tuple with two fields: ``statistic`` and ``pvalue``.



For a simple example consider the hypothesis that the sample (.4, .1, .7) comes

from the uniform distribution on [0, 1]:



.. code:: python



    if ks_test((.4, .1, .7), unif(0, 1)).pvalue < .05:

        print("Hypothesis rejected with 5% significance.")



If your samples are very large and you have them sorted ahead of time, pass

``assume_sorted=True`` to save some time that would be wasted resorting.



Extending

=========



Simple tests are composed of two phases: calculating the test statistic and

determining how likely is the resulting value (under the hypothesis).

New tests may be defined by providing a new statistic calculation routine or an

alternative distribution for a statistic.



Functions calculating statistics are given evaluations of the reference

cumulative distribution function on sorted data and are expected to return

a single number.

For a simple test, if the sample indeed comes from the hypothesized (continuous)

distribution, the values passed to the function should be uniformly distributed

over [0, 1].



Here is a simplistic example of how a statistic function might look like:



.. code:: python



    def ex_stat(data):

        return abs(data.sum() - data.size / 2)



Statistic functions for the provided tests, ``ks_stat()``, ``cvm_stat()``,

and ``ad_stat()``, can be imported from ``skgof.ecdfgof``.



Statistic distributions should derive from ``rv_continuous`` and implement

at least one of the abstract ``_cdf()`` or ``_pdf()`` methods (you might

also consider directly coding ``_sf()`` for increased precision of results

close to 1). For example:



.. code:: python



    from numpy import sqrt

    from scipy.stats import norm, rv_continuous



    class ex_unif_gen(rv_continuous):

        def _cdf(self, statistic, samples):

            return 1 - 2 * norm.cdf(-statistic, scale=sqrt(samples / 12))



    ex_unif = ex_unif_gen(a=0, name='ex-unif', shapes='samples')



The provided distributions live in separate modules, respectively ``ksdist``,

``cvmdist``, and ``addist``.



Once you have a statistic calculation function and a statistic distribution the

two parts can be combined using ``simple_test``:



.. code:: python



    from functools import partial

    from skgof.ecdfgof import simple_test



    ex_test = partial(simple_test, stat=ex_stat, pdist=ex_unif)



**Exercise**: The example test has a fundamental flaw. Can you point it out?



..  The test is not consistent under all alternatives. For instance, if the

    hypothesis was that samples come from the uniform distribution on [0, 1],

    but they really were "drawn" from the degenerate distribution at .5, the

    test would never notice, even for arbitrarily large sample sizes.



    Moreover, the asymptotic distribution is not a good approximation of the

    actual statistic distribution for small sample sizes.



Installation

============



.. code:: bash



    pip install scikit-gof



Requires recent versions of Python (> 3), NumPy (>= 1.10) and SciPy.



Please fix or point out any errors, inaccuracies or typos you notice.