Communications in Statistics - Theory and Methods, ( ISI ), Volume (48), No (18), Year (2018-9) , Pages (4569-4580)

Title : ( Sequential order statistics from dependent random variables )

Authors: Mohammad Baratnia , Mahdi Doostparast ,

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Abstract

‎This paper provides an extension for ``sequential order statistics\\\'\\\' (SOS) introduced by KAMPS. ‎It is called ``developed sequential order statistics\\\'\\\' (DSOS) and is useful for describing lifetimes of engineering systems when component lifetimes are dependent‎. ‎Explicit expressions for the joint density function‎, ‎the marginal distributions and the means of DSOS are derived‎. ‎Under the well known ``conditional proportional hazard rate\\\'\\\' (CPHR) model and the Gumbel families of copulas for dependency among component lifetimes‎, ‎some findings are reported‎. ‎For example‎, ‎it is proved that the joint density functions of DSOS and SOS have the same structure‎. ‎Various illustrative examples are also given‎.

Keywords

, ‎Sequential order statistics‎, ‎Lifetime models‎, ‎r-out-of-n system‎, ‎Gumbel copula; Estimation‎.