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I am trying to use chi-square distance to find the similarity between two PDFs. My data is chi-square distributed. though the chi-square distance works well but my question is can I use the jensen-shannon distance with Chi-square distributed data?. I have tried the Jensen-Shannon distance but I have the zero division problem when certain bins of the histogram have zero frequency. Is it because my data is not normally distributed? Any help would be highly appreciated. Thanks

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  • $\begingroup$ It is hard to provide a definitive answer without knowing more context about your dataset - for example, is it discrete/continuous? With this in mind, and taking a more generalized perspective, maybe you could consider using the Hellinger Distance (en.wikipedia.org/wiki/Hellinger_distance) to a measure of similarity between the two PDFs. It has some nice properties, such as being a true metric and being bounded on the closed interval [0,1]. It is also a simple calculation and relatively intuitive. Importantly for your application, it isn't limited by 'the zero division problem'. $\endgroup$
    – Mari153
    Sep 29, 2022 at 11:00

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