Exponential monomials on Sturm-Liouville hypergroups.

Vajday, L.

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This article studies exponential families $ℰ$ on finite sets such that the information divergence $D (P ∥ ℰ)$ of an arbitrary probability distribution from $ℰ$ is bounded by some constant $D > 0$ . A particular class of low-dimensional exponential families that have low values of $D$ can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. The case where $D = log (2)$ is studied in detail. This case is special, because if $D < log (2)$ , then $ℰ$ contains...