Author

• Mohammad Khanjari Sadegh

Department of Statistics‎, ‎University of Birjand‎, ‎Birjand‎, ‎Iran

Abstract

Let T1,...,Tn be exchangeable random variables and suppose that T{1:n} represents the ith order statistic among Ti's, i=1,...,n. ‎In this paper some expressions for the joint distribution ‎of (T{1:n},...,T{n:n}), ‎marginal distribution of T{1:n} and the joint distribution of (T{r:n},T{k:n}), 1≤ r ≤ k ≤n ‎in terms of the joint distribution (or joint reliability) function of Ti's are provided. ‎Using these and when {T1,...,Tn} is a sequence of‎ ‎lifetimes, some expressions for the mean residual life functions of a n-k+1-out-of-n system‎, Hnk(t)=E(T{k:n}-t|T{1:n}>t) and Mn{r,k}(t)=E(T{k:n}-t|T{r:n}>t), ‎1≤ r≤ k≤ n in terms of the joint survival function of Ti's are given‎. ‎Also, ‎some examples are provided‎. 

Keywords

• DFR‎
• ‎Exchangeable random variables‎
• ‎IFR‎
• ‎Mean residual life function‎
• ‎Order‎ ‎statistics‎
• ‎(n-k+1)-out-of-n system