ORDER STATISTICS FROM DEPENDENT, COMPLETELY MONOTONE DISTRIBUTIONS

We consider order statistics corresponding to X1, . . . , Xn, where Xi ∼ λ −1 I 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 Eλ −1 i < ∞. Thus, λ1, . . . , λn, can be interpreted as random failure rates, and their dependency might be due to common environmental factors.