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Consider two probability distributions P and Q defined on the same probability space X. Does the following similarity measure have a name?

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Context: I "invented" this formula to compare binding-sequence statistics of proteins and would like to check the validity of this approach and read up on alternatives.

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I'm not sure what this is called, but to me it looks like your expression is related to the hellinger distance H(P, Q) via $$\mathrm{similarity(P, Q)} = 1-H^2(P, Q)$$.

Maybe this will help: https://en.wikipedia.org/wiki/Hellinger_distance#Discrete_distributions

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    $\begingroup$ Note the name is on that page (although the formula is not as obvious on that page is it perhaps should be). It is the Bhattacharyya Coefficient. $\endgroup$
    – Mark Schultz-Wu
    Commented Aug 9, 2022 at 13:58
  • $\begingroup$ Bhattacharyya Coefficient - That's it! Very helpful! $\endgroup$
    – KaPy3141
    Commented Aug 9, 2022 at 14:48

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