Limit distributions of the upper order statistics for the L\'evy-frailty Marshall-Olkin distribution

In this paper we give the precise asymptotic behavior of the upper-order statistics of the L\'evy-frailty Marshall-Olkin (LFMO) distribution. Our main result is a CLT-type theorem showing that the upper-order statistics converge in distribution after a certain logarithmic centering and scaling, when assuming that the underlying L\'evy subordinator process is in the normal domain of attraction of a Stable distribution. Our result is especially useful in network reliability and systemic risk, when modeling the lifetimes of the components in a system using the LFMO distribution, as it allows to give easily computable confidence intervals for the lifetimes of components.