{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T04:42:31Z","timestamp":1780980151756,"version":"3.54.1"},"reference-count":28,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T00:00:00Z","timestamp":1719964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Brasilia","award":["01\/2024"],"award-info":[{"award-number":["01\/2024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Asymmetric distributions are frequently seen in real-world datasets due to a number of factors, such as sample biases and nonlinear interactions between the variables observed. Thus, in order to better characterize real-world phenomena, studying asymmetric distribution is of great interest. In this work, we derive stress\u2013strength reliability formulas of the type P(X&lt;Y) when both X and Y follow p-max stable laws with three parameters, which are inherently asymmetric. The new relations are given in terms of extreme-value H-functions and have been obtained under fewer parameter restrictions when compared to similar results in the literature. We estimate the parameters of the p-max stable laws by a stochastic optimization method and the stress\u2013strength probability by a maximum likelihood procedure. The performance of the analytical models is evaluated through simulations and real-life dataset modeling.<\/jats:p>","DOI":"10.3390\/sym16070837","type":"journal-article","created":{"date-parts":[[2024,7,3]],"date-time":"2024-07-03T09:23:59Z","timestamp":1719998639000},"page":"837","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Estimation of P(X &lt; Y) Stress\u2013Strength Reliability Measures for a Class of Asymmetric Distributions: The Case of Three-Parameter p-Max Stable Laws"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0286-0541","authenticated-orcid":false,"given":"Felipe Sousa","family":"Quintino","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9790-369X","authenticated-orcid":false,"given":"Pushpa Narayan","family":"Rathie","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2581-0486","authenticated-orcid":false,"given":"Luan Carlos de Sena Monteiro","family":"Ozelim","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, University of Brasilia, Brasilia 70910-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-5147-4393","authenticated-orcid":false,"given":"Tiago Alves","family":"da Fonseca","sequence":"additional","affiliation":[{"name":"Gama Engineering College, University of Brasilia, Brasilia 70910-900, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kotz, S., Lumelskii, Y., and Pensky, M. 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