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Here, we first discuss a count distribution derived as a discrete analogue of the continuous half-logistic distribution, which is obtained by preserving the expression of its survival function at each non-negative integer support point. The proposed discrete distribution has a mode at zero and allows for over-dispersion; these two features make it suitable for modeling purposes in many fields (e.g., insurance and ecology), when these conditions are satisfied by the data. In order to widen its spectrum of applications, a discrete analogue is also presented of the type\u00a0I generalized half-logistic distribution (obtained by adding a shape parameter to the simple one-parameter half-logistic), which allows us to model count data whose mode is not necessarily zero. For these new count distributions, the main statistical properties are outlined, and parameter estimation along with related issues is discussed. Their feasibility is proved on two real data sets taken from the literature, which have already been fitted by other well-established count distributions. Finally, a possible application is illustrated in the insurance field, related to the exact\/approximate determination of the distribution of the total claims amount through the well-known Panjer\u2019s recursive formula, within the framework of collective risk models.<\/jats:p>","DOI":"10.1007\/s10479-023-05807-3","type":"journal-article","created":{"date-parts":[[2024,1,19]],"date-time":"2024-01-19T19:02:11Z","timestamp":1705690931000},"page":"27-57","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Discrete half-logistic distributions with applications in reliability and risk analysis"],"prefix":"10.1007","volume":"340","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5072-5662","authenticated-orcid":false,"given":"Alessandro","family":"Barbiero","sequence":"first","affiliation":[]},{"given":"Asmerilda","family":"Hitaj","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,19]]},"reference":[{"issue":"4","key":"5807_CR1","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1080\/00949658508810784","volume":"20","author":"N Balakrishnan","year":"1985","unstructured":"Balakrishnan, N. 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