Distribution of Order Statistics for Exchangeable Random Variables

Let T1,...,Tn be exchangeable random variables and suppose that T{1:n} represents the ith order statistic among Tis, i=1,...,n. ýIn this paper some expressions for the joint distribution ýof (T{1:n},...,T{n:n}), ýmarginal distribution of T{1:n} and the joint distribution of (T{r:n},T{k:n}), 1≤ r ≤ k ≤n ýin terms of the joint distribution (or joint reliability) function of Ti's are provided. ýUsing these and when {T1,...,Tn} is a sequence ofý ýlifetimes, some expressions for the mean residual life functions of a n-kout-of-n systemý, 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), ý1≤ r≤ k≤ n in terms of the joint survival function of Ti's are givený. ýAlso, ýsome examples are providedý.