ORDER STATISTICS FROM DEPENDENT, COMPLETELY MONOTONE DISTRIBUTIONS

We consider order statistics corresponding to X-1,...,X-n, where X-i similar to lambda(-1)(i) epsilon, i = 1,...,n, epsilon(1),...,epsilon(n) are independent and identically distributed exponentials with mean 1, and lambda(1),...,lambda(n) are possibly dependent, possibly nonidentically distributed, positive random variables, with E lambda(-1)(i) < infinity. Thus, lambda(1),...,lambda(n,) can be interpreted as random failure rates, and their dependency might be due to common environmental factors.