Unimodal Category and Topological Statistics
نویسندگان
چکیده
We consider the problem of decomposing a compactly supported distribution f : Rn → [0,∞) into a minimal number of unimodal components by means of some convex operation (e.g., sum or sup). The resulting “unimodal category” of f is a topological invariant of the distribution which shares a number of properties with the Lusternik-Schnirelmann category of a topological space. This work introduces the concept of a unimodal category, provides fundamental examples (lp unimodal category), and computes various unimodal categories for distributions on Rn with n small.
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