Fractional Moments and Maximum Entropy: Geometric Meaning

Henryk Gzyl (), Pier Luigi Novi Inverardi and Aldo Tagliani

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 17, 3596-3601

Abstract: We consider the problem of recovering a probability density on a bounded or unbounded subset D of [0, ∞), from the knowledge of its sequence of fractional moments within a maximum entropy (MaxEnt) setup. Based upon entropy convergence results previously formulated, the fractional moments are selected so that the entropy of the MaxEnt approximation be minimum. A geometric interpretation of the reconstruction procedure is formulated as follows: the two moment curves generated by the unknown density and its MaxEnt approximation are interpolating in Hermite-Birkoff sense; that is, they are both interpolating and tangent at the selected nodes.

Date: 2014
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DOI: 10.1080/03610926.2012.705212

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