How can we use shannon entropy to discriminate between two similar probability distribution function? I studied two papers related to discriminating between two similar distributions using Shannon entropy. But both of them had different views. Can anyone explain what would be the basic flow of idea to for discrimination procedure using Shannon entropy as a statistic?
Here are the two papers:
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I have only skimmed the papers, and I am not sure about what you mean by "discrimination", but my impression is that the authors of those papers use entropy to "discriminate" distributions following the idea of the Maximum Entropy Principle. That approach says that, if I have several distributions that all satisfy my constraints, I should choose the one with maximum entropy, since that way I make the least assumptions, i.e. sampling results in "maximum surprise".
If you are more generally interested in the discrimination of distributions in the sense of assigning some kind of distance to a given pair of distributions, you could have a look at relative entropy, Bregman divergence, or Wasserstein metric. For a list of popular choices, see here.
