Limit distributions of the upper order statistics for the Levy-frailty Marshall-Olkin distribution
Barrera
J
author
Lagos
G
author
2020
English
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.
Marshall-Olkin distribution
Dependent random variables
Upper order statistics
Extreme-value theory
Reliability
WOS:000557129100001
exported from refbase (show.php?record=1218), last updated on Wed, 12 Jan 2022 10:09:08 -0300
text
10.1007/s10687-020-00386-z
Barrera+Lagos2020
Extremes
Extremes
2020
Springer
continuing
periodical
academic journal
23
603
628
1386-1999