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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]

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]