Stieltjes and Hamburger Reduced Moment Problem When MaxEnt Solution Does Not Exist Article Swipe

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Principle of maximum entropy Riemann–Stieltjes integral Moment (physics) Mathematics Distribution (mathematics) Set (abstract data type) Entropy (arrow of time) Statistical physics Applied mathematics Computer science Mathematical optimization Mathematical analysis Statistics Physics Integral equation Thermodynamics Classical mechanics Programming language

Pier Luigi Novi Inverardi , Aldo Tagliani ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.3390/math9040309 · OA: W3126550870

For a given set of moments whose predetermined values represent the available information, we consider the case where the Maximum Entropy (MaxEnt) solutions for Stieltjes and Hamburger reduced moment problems do not exist. Genuinely relying upon MaxEnt rationale we find the distribution with largest entropy and we prove that this distribution gives the best approximation of the true but unknown underlying distribution. Despite the nice properties just listed, the suggested approximation suffers from some numerical drawbacks and we will discuss this aspect in detail in the paper.