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