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Author Barrera, J., Lagos, G.
Title Limit distributions of the upper order statistics for the Levy-frailty Marshall-Olkin distribution Type
Year 2020 Publication Extremes Abbreviated Journal Extremes
Volume 23 Issue Pages 603-628
Keywords Marshall-Olkin distribution; Dependent random variables; Upper order statistics; Extreme-value theory; Reliability
Abstract The Marshall-Olkin (MO) distribution is considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of dependent components or entities of a system and dependency is induced by “shocks” that hit one or more components at a time. Of particular interest is the Levy-frailty subfamily of the Marshall-Olkin (LFMO) distribution, since it has few parameters and because the nontrivial dependency structure is driven by an underlying Levy subordinator process. The main contribution of this work is that we derive the precise asymptotic behavior of the upper order statistics of the LFMO distribution. More specifically, we consider a sequence ofnunivariate random variables jointly distributed as a multivariate LFMO distribution and analyze the order statistics of the sequence asngrows. Our main result states that if the underlying Levy subordinator is in the normal domain of attraction of a stable distribution with index of stability alpha then, after certain logarithmic centering and scaling, the upper order statistics converge in distribution to a stable distribution if alpha> 1 or a simple transformation of it if alpha <= 1. Our result can also give easily computable confidence intervals for the last failure times, provided that a proper convergence analysis is carried out first.
Address [Barrera, Javiera; Lagos, Guido] Univ Adolfo Ibanez, Fac Engn & Sci, Av Diagonal Las Torres 2640, Santiago, Chile, Email: javiera.barrera@uai.cl;
Corporate Author Thesis
Publisher Springer Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 1386-1999 ISBN Medium
Area Expedition Conference
Notes WOS:000557129100001 Approved
Call Number UAI @ eduardo.moreno @ Serial 1218
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