{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T01:55:33Z","timestamp":1776822933687,"version":"3.51.2"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T00:00:00Z","timestamp":1632787200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["PD\/BD\/150459\/2019"],"award-info":[{"award-number":["PD\/BD\/150459\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007474","name":"Centro de Matem\u00e1tica, Universidade de Coimbra","doi-asserted-by":"publisher","award":["UIDB\/00324\/2020"],"award-info":[{"award-number":["UIDB\/00324\/2020"]}],"id":[{"id":"10.13039\/501100007474","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Prob. Eng. Inf. Sci."],"published-print":{"date-parts":[[2023,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The star-shaped ordering between probability distributions is a common way to express aging properties. A well-known criterion was proposed by Saunders and Moran [(1978). On the quantiles of the gamma and F distributions.<jats:italic>Journal of Applied Probability<\/jats:italic>15(2): 426\u2013432], to order families of distributions depending on one real parameter. However, the lifetime of complex systems usually depends on several parameters, especially when considering heterogeneous components. We extend the Saunders and Moran criterion characterizing the star-shaped order when the multidimensional parameter moves along a given direction. A few applications to the lifetime of complex models, namely parallel and series models assuming different individual components behavior, are discussed.<\/jats:p>","DOI":"10.1017\/s0269964821000449","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T04:48:51Z","timestamp":1632804531000},"page":"49-59","source":"Crossref","is-referenced-by-count":4,"title":["Star-shaped order for distributions characterized by several parameters and some applications"],"prefix":"10.1017","volume":"37","author":[{"given":"Idir","family":"Arab","sequence":"first","affiliation":[]},{"given":"Milto","family":"Hadjikyriakou","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7217-5705","authenticated-orcid":false,"given":"Paulo Eduardo","family":"Oliveira","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0606-2953","authenticated-orcid":false,"given":"Beatriz","family":"Santos","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"S0269964821000449_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4266(86)80003-6"},{"key":"S0269964821000449_ref17","doi-asserted-by":"publisher","DOI":"10.2307\/3213414"},{"key":"S0269964821000449_ref1","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964817000481"},{"key":"S0269964821000449_ref9","first-page":"466","article-title":"Ordering convolutions of gamma random variables","volume":"66","author":"Khaledi","year":"2004","journal-title":"Sankhy\u0101: The Indian Journal of Statistic"},{"key":"S0269964821000449_ref7","doi-asserted-by":"publisher","DOI":"10.1080\/03610929808832134"},{"key":"S0269964821000449_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s11009-019-09740-6"},{"key":"S0269964821000449_ref16","volume-title":"Life distributions","author":"Marshall","year":"2007"},{"key":"S0269964821000449_ref4","volume-title":"Statistical theory of reliability and life testing: Probability models","author":"Barlow","year":"1975"},{"key":"S0269964821000449_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0021900200007762"},{"key":"S0269964821000449_ref6","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression models and life tables (with discussion)","volume":"34","author":"Cox","year":"1972","journal-title":"Journal of the Royal Statistical Society: Series B (Statistical Methodology)"},{"key":"S0269964821000449_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-012-1212-4"},{"key":"S0269964821000449_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/apr.2020.6"},{"key":"S0269964821000449_ref14","doi-asserted-by":"publisher","DOI":"10.1002\/0471722065"},{"key":"S0269964821000449_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2010.06.019"},{"key":"S0269964821000449_ref8","volume-title":"Total positivity","volume":"1","author":"Karlin","year":"1968"},{"key":"S0269964821000449_ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964812000071"},{"key":"S0269964821000449_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2012.12.025"},{"key":"S0269964821000449_ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-34675-5"},{"key":"S0269964821000449_ref19","doi-asserted-by":"publisher","DOI":"10.2307\/2533515"}],"container-title":["Probability in the Engineering and Informational Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0269964821000449","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T21:55:04Z","timestamp":1725832504000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0269964821000449\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,28]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,1]]}},"alternative-id":["S0269964821000449"],"URL":"https:\/\/doi.org\/10.1017\/s0269964821000449","relation":{},"ISSN":["0269-9648","1469-8951"],"issn-type":[{"value":"0269-9648","type":"print"},{"value":"1469-8951","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,28]]}}}