Stochastic Comparisons 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 X1,...,Xn [Y1,...,Yn] be independent exponential random variables with X1,...,XP [Yi,..., Yp] having common hazard rate λ1 [λ1*] and Xp+1,...,Xn [Yp+1,...,Yn] having common hazard rate λ2 [λ2*]. Let D2:n and D2*:n denote the corresponding second sample spacing, respectively. It is proved here that D2:n is stochastically greater than D2:n* in the sense of the likelihood ratio order, under two different kinds of parameter conditions. These results established here strengthen and generalize some of the results known in the literature. Some applications are also presented to illustrate the results.