{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T13:30:36Z","timestamp":1772458236729,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T00:00:00Z","timestamp":1668384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Romanian Ministery of Education and Research, CNCS\u2014UEFISCDI","award":["PN-III-P4-ID-PCE-2020-1112"],"award-info":[{"award-number":["PN-III-P4-ID-PCE-2020-1112"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The aim of this paper consists in developing an entropy-based approach to risk assessment for actuarial models involving truncated and censored random variables by using the Tsallis entropy measure. The effect of some partial insurance models, such as inflation, truncation and censoring from above and truncation and censoring from below upon the entropy of losses is investigated in this framework. Analytic expressions for the per-payment and per-loss entropies are obtained, and the relationship between these entropies are studied. The Tsallis entropy of losses of the right-truncated loss random variable corresponding to the per-loss risk model with a deductible d and a policy limit u is computed for the exponential, Weibull, \u03c72 or Gamma distribution. In this context, the properties of the resulting entropies, such as the residual loss entropy and the past loss entropy, are studied as a result of using a deductible and a policy limit, respectively. Relationships between these entropy measures are derived, and the combined effect of a deductible and a policy limit is also analyzed. By investigating residual and past entropies for survival models, the entropies of losses corresponding to the proportional hazard and proportional reversed hazard models are derived. The Tsallis entropy approach for actuarial models involving truncated and censored random variables is new and more realistic, since it allows a greater degree of flexibility and improves the modeling accuracy.<\/jats:p>","DOI":"10.3390\/e24111654","type":"journal-article","created":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T02:28:58Z","timestamp":1668479338000},"page":"1654","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Tsallis Entropy for Loss Models and Survival Models Involving Truncated and Censored Random Variables"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0686-3718","authenticated-orcid":false,"given":"Vasile","family":"Preda","sequence":"first","affiliation":[{"name":"\u201cGheorghe Mihoc-Caius Iacob\u201d Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania"},{"name":"\u201cCostin C. Kiri\u0163escu\u201d National Institute of Economic Research, 050711 Bucharest, Romania"},{"name":"Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7195-0941","authenticated-orcid":false,"given":"Silvia","family":"Dedu","sequence":"additional","affiliation":[{"name":"\u201cCostin C. Kiri\u0163escu\u201d National Institute of Economic Research, 050711 Bucharest, Romania"},{"name":"Department of Applied Mathematics, Bucharest University of Economic Studies, 010734 Bucharest, Romania"}]},{"given":"Iuliana","family":"Iatan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Technical University of Civil Engineering, 020396 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3142-2225","authenticated-orcid":false,"given":"Ioana D\u0103nil\u0103","family":"Cernat","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9213-0616","authenticated-orcid":false,"given":"Muhammad","family":"Sheraz","sequence":"additional","affiliation":[{"name":"Institute of Business Administration Karachi, Department of Mathematical Sciences, School of Mathematics and Computer Science, Karachi 75270, Pakistan"},{"name":"Department Financial Mathematics, Fraunhofer ITWM, Fraunhofer-Platz, 67663 Kaiserslautern, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,14]]},"reference":[{"key":"ref_1","first-page":"688","article-title":"On Entropy-type Measures and Divergences with Applications in Engineering, Management and Applied Sciences","volume":"6","author":"Koukoumis","year":"2021","journal-title":"Int. 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