{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:14:52Z","timestamp":1760145292671,"version":"build-2065373602"},"reference-count":71,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,30]],"date-time":"2024-06-30T00:00:00Z","timestamp":1719705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper establishes a general framework for measuring statistical divergence. Namely, with regard to a pair of random variables that share a common range of values: quantifying the distance of the statistical distribution of one random variable from that of the other. The general framework is then applied to the topics of socioeconomic inequality and renewal processes. The general framework and its applications are shown to yield and to relate to the following: f-divergence, Hellinger divergence, Renyi divergence, and Kullback\u2013Leibler divergence (also known as relative entropy); the Lorenz curve and socioeconomic inequality indices; the Gini index and its generalizations; the divergence of renewal processes from the Poisson process; and the divergence of anomalous relaxation from regular relaxation. Presenting a \u2018fresh\u2019 perspective on statistical divergence, this paper offers its readers a simple and transparent construction of statistical-divergence gauges, as well as novel paths that lead from statistical divergence to the aforementioned topics.<\/jats:p>","DOI":"10.3390\/e26070565","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T05:08:34Z","timestamp":1719896914000},"page":"565","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Statistical Divergence and Paths Thereof to Socioeconomic Inequality and to Renewal Processes"],"prefix":"10.3390","volume":"26","author":[{"given":"Iddo","family":"Eliazar","sequence":"first","affiliation":[{"name":"School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hao, L., and Naiman, D.Q. 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