Provides variants of Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling goodness of fit tests for fully specified continuous distributions.
>>> 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...)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()withalternative='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]:
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.
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:
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:
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:
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?
pip install scikit-gofRequires recent versions of Python (> 3), NumPy (>= 1.10) and SciPy.
Please fix or point out any errors, inaccuracies or typos you notice.