Variations on goodness of fit tests for SciPy.
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:
- Kolmogorov-Smirnov supremum statistic; almost the same as scipy.stats.kstest() with alternative='two-sided' but with (hopefully) somewhat more precise p-value calculation;
- Cramer-von Mises L2 statistic, with a rather crude estimation of the statistic distribution (but seemingly the best available);
- 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-gof
Requires recent versions of Python (> 3), NumPy (>= 1.10) and SciPy.
Please fix or point out any errors, inaccuracies or typos you notice.