151. Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities.
- Author
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Stoyanov, Jordan M., Tagliani, Aldo, and Novi Inverardi, Pier Luigi
- Subjects
- *
ENTROPY , *CONTINUOUS distributions , *DISTRIBUTION (Probability theory) , *DENSITY , *HAMBURGERS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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