{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T13:37:31Z","timestamp":1772113051329,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T00:00:00Z","timestamp":1706572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Bulgarian Ministry of Education and Science PIKOM","award":["DO 1-67\/05.05.2022"],"award-info":[{"award-number":["DO 1-67\/05.05.2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e26020121","type":"journal-article","created":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T11:35:34Z","timestamp":1706614534000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities"],"prefix":"10.3390","volume":"26","author":[{"given":"Jordan M.","family":"Stoyanov","sequence":"first","affiliation":[{"name":"Institute of Mathematics & Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria"},{"name":"Faculty of Mathematical Sciences, Shandong University, Jinan 250100, China"}]},{"given":"Aldo","family":"Tagliani","sequence":"additional","affiliation":[{"name":"Department of Economics & Management, University of Trento, 38100 Trento, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3704-6921","authenticated-orcid":false,"given":"Pier Luigi","family":"Novi Inverardi","sequence":"additional","affiliation":[{"name":"Department of Economics & Management, University of Trento, 38100 Trento, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Novi Inverardi, P.L., Tagliani, A., and Stoyanov, J.M. 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