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Probability inequalities via negative dependence for random variables conditioned on order statistics
Authors:Henry W. Block  Vanderlei Bueno  Thomas H. Savits  Moshe Shaked
Abstract:Distributions are studied which arise by considering independent and identically distributed random variables conditioned on events involving order statistics. It is shown that these distributions are negatively dependent in a very strong sense. Furthermore, bounds are found on the distribution functions. The conditioning events considered occur naturally in reliability theory as the time to system failure for k-out-of-n systems. An application to systems formed with “second-hand” components is given.
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