ORDER STATISTICS FROM DEPENDENT, COMPLETELY MONOTONE DISTRIBUTIONS

Abstract

We consider order statistics corresponding to X1, …, Xn, where $X_{i} \sim \lambda_{i}^{-1} \cal{E}$, i = 1, …, n, ℰ1, …, ℰn are independent and identically distributed exponentials with mean 1, and λ1, …, λn are possibly dependent, possibly nonidentically distributed, positive random variables, with $E\lambda_{i}^{-1} < \infty$. Thus, λ1, …, λn, can be interpreted as random failure rates, and their dependency might be due to common environmental factors.