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oai:recercat.cat:2117/4425002026-01-21T04:25:45Zcom_2072_1033col_2072_452950

On statistical model extensions based on randomly stopped extremes Valero Baya, Jordi Ginebra Molins, Josep Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa Universitat Politècnica de Catalunya. ADBD - Anàlisi de Dades Complexes per a les Decisions Empresarials Àrees temàtiques de la UPC::Matemàtiques i estadística Marshall-Olkin extension Extreme value Randomly stopped maximum Randomly stopped minimum Statistical stability Stopping model. The maxima and the minima of a randomly stopped sample of a random variable, X, together with two newly defned random variables that make X into the maxima or minima of a randomly stopped sample of them, can be used to defne statistical model transformation mechanisms. These transformations can be used to defne models for extreme-value data that are not grounded on large sample theory. The relationship between the stopping model and characteristics of the corresponding model transformations obtained is investigated. In particular, one looks into which stopping models make these model transformations into model extensions, and which stopping models lead to statistically stable extensions in the sense that using the model extension a second time leaves the extended model unchanged. The stopping models under which the extensions based on randomly stopped maxima and their inverses coincide with the extensions based on randomly stopped minima and their inverses are also characterized. The advantages of using models obtained through these model extension mechanisms instead of resorting to extreme-value models grounded on asymptotic arguments is illustrated by way of examples. Peer Reviewed Postprint (published version) 2025-01-01 Article Valero, J.; Ginebra, J. On statistical model extensions based on randomly stopped extremes. «Sort (Barcelona)», 1 Gener 2025, vol. 49, núm. 1, p. 43-72. 1696-2281 https://hdl.handle.net/2117/442500 10.57645/20.8080.02.22 eng https://www.idescat.cat/sort/sort491/49.1.2.Valero-Ginebra.pdf Open Access 30 p. application/pdf