Abstract
It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy ∝ fh i dμ = λ i for i = 1, 2, ..., ... kthe maximizer of entropy is an f 0 that is proportional to exp(Σc i h i ) for some choice of c i . An extension of this to a continuum of constraints and many examples are presented.
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Athreya, K.B. Entropy maximization. Proc Math Sci 119, 531–539 (2009). https://doi.org/10.1007/s12044-009-0049-5
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DOI: https://doi.org/10.1007/s12044-009-0049-5