Exploiting The Waiting Time Paradox: Applications Of The Size-Biasing Transformation
Probability in the Engineering and Informational Sciences
Introduction to Probability Models, Ninth Edition
Introduction to Probability Models, Ninth Edition
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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} . Thus, λ1, …, λn, can be interpreted as random failure rates, and their dependency might be due to common environmental factors.