For a given set of univariate integer data fit a number of discrete distributions and give information about the fits. The current distributions used are:
- discrete uniform (not really a fit then)
- beta binomial
- zipfian
as implemented by scipy
- scipy 1.9.0
> python fit_discrete.py test_data.txt
Successfully fitted the discrete uniform distribution:
the fit parameters are: FitParams(low=1.0, high=4.0, loc=0.0)
the negative log likelihood is: 6.591673732008659
Successfully fitted the beta binomial distribution:
the fit parameters are: FitParams(n=2.0, a=0.9999990554067835, b=1.9999982152999867, loc=1.0)
the negative log likelihood is: 6.068425588244196
Successfully fitted the zipfian distribution:
the fit parameters are: FitParams(a=2.2195448757323435, loc=0.0)
the negative log likelihood is: 7.86098064513523
The goodness of fit is determined here using the maximum likehood approach. The fit itself is done by scipy.stats.fit which optimises for the parameters that maximise the likelyhood estimate. Note, scipy.stats.fit is a new feature introduced in scipy 1.9.0 that allows seamless fitting both discrete and continuous distributions.
The goodness of fit metric shown here is the negative log of the Probability Mass Function (PMF).
Fitting requires some rough information about parameters bounds or a guess value to start from. Here, I hardcoded very rough bounds that could very well fail for a variety of data edge cases. These bounds were tested on datasets sampled from uniform distributions.
The script could easily be extended to fit any other scipy discrete distribution. If additional distributions are required one would have to manually write the distribution function, and then manually find the parameters that maximise the PMF.
Ideally, the choice of distributions would not be hardcoded and the user could choose based on looking at their data what distributions to try.