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 $\int fh_id_\mu=\lambda_i$ for $i=1,2,\ldots,\ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $\exp(\sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.
K B Athreya1 2
Volume 129 | Issue 5
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