Stoyanov JM, Tagliani A, Novi Inverardi PL. Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities.
Entropy (Basel) 2024;
26:121. [PMID:
38392376 PMCID:
PMC10888222 DOI:
10.3390/e26020121]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Revised: 01/29/2024] [Accepted: 01/29/2024] [Indexed: 02/24/2024]
Abstract
We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy.
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