Likelihood ratio order of the second spacing in multiple-outlier exponential models

In this paper, we study the ordering properties of the second sample spacing arising from multiple-outlier exponential models in terms of the likelihood ratio order. Let [] be independent exponential random variables with [] having common hazard rate [] and [] having common hazard rate []. Let and denote the corresponding second sample spacing, respectively. It is proved here that is stochastically greater than in the sense of the likelihood ratio order, under two different kinds of parameter conditions. The results established here strengthen and generalize some of the results known in the literature. Two applications are also presented to illustrate the results.