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.
Khanjari Sadegh,M . (2022). Distribution of Order Statistics for Exchangeable Random Variables. Journal of the Iranian Statistical Society, 15(1), 59-70.
MLA
Khanjari Sadegh,M . "Distribution of Order Statistics for Exchangeable Random Variables", Journal of the Iranian Statistical Society, 15, 1, 2022, 59-70.
HARVARD
Khanjari Sadegh M. (2022). 'Distribution of Order Statistics for Exchangeable Random Variables', Journal of the Iranian Statistical Society, 15(1), pp. 59-70.
CHICAGO
M Khanjari Sadegh, "Distribution of Order Statistics for Exchangeable Random Variables," Journal of the Iranian Statistical Society, 15 1 (2022): 59-70,
VANCOUVER
Khanjari Sadegh M. Distribution of Order Statistics for Exchangeable Random Variables. JIRSS. 2022;15(1):59-70.
Journal of the Iranian Statistical Society