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In this paper, we investigate some stochastic comparisons in terms of likelihood ratio ordering between spacings from independent random variables exponentially distributed with different scale parameters. We partially solve some open problems in [Wen S, Lu Q, Hu T. Likelihood ratio orderings of spacings of heterogeneous exponential random variables. J Multivariate Anal. 2007;98:743–756] for a one-sample problem and in [Hu T, Lu Q, Wen S. Stochastic comparisons and dependence of spacings from two samples of exponential random variables. Commun Stat – Theory Methods 2006;35:979–988] for a two-sample problem. Specifically, we prove that the second spacing is always smaller than the third spacing in terms of the likelihood ratio order and we provide the ordering among all spacings in the casen=4. In the two-sample case, we establish comparisons between the second spacings related to each sample under certain conditions. [ABSTRACT FROM AUTHOR]

In this paper, comparisons of allocation policies of components in two-parallel-series systems with two types of components are provided with respect to both hazard rate and reversed hazard rate orders. The main results indicate that the lifetime of these kinds of system is stochastically maximized by unbalancing the two classes of components as much as possible. We only assume that the two distributions implied in the model have proportional hazard rates. The same type of comparisons are also given for the dual model, the two-series-parallel systems, but assuming that the distributions implied in the model have proportional reversed hazard rates, and therefore the final conclusion is the opposite; that is, the reliability of the system improves as the similarity between the two parallel subsystems increases. [ABSTRACT FROM PUBLISHER]

Abstract: In this article we obtain some new results in the area of stochastic comparisons of simple and normalized spacings from two samples of heterogeneous exponential random variables. Specifically, we investigate conditions under which successive spacings are ordered in the likelihood ratio ordering. We also show some applications of our results to the multiple-outlier case. [Copyright &y& Elsevier]

Abstract: Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied and also an application in reliability theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t 0 aging notion. [Copyright &y& Elsevier]

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory and finance are described. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we partially solve a conjecture by Kochar and Korwar (1996) in relation to the normalized spacings of the order statistics of a sample of independent exponential random variables with different scale parameters. In the case of a sample of size , they proved the ordering of the normalized spacings and conjectured that result holds for all . We prove this conjecture for for both spacings and normalized spacings and generalize some results to . [Copyright &y& Elsevier]