On stochastic comparisons of residual life time at random time

Let X 1 , X 2 , Θ and Θ ′ be independent non-negative random variables. The residual life of X i at random time Θ , that is, X i Θ = X i − Θ ∣ X i > Θ is considered. Some sufficient conditions which lead to the likelihood ratio ordering, the failure rate ordering, the reverse failure rate orderin...
Ausführliche Beschreibung

Let X 1 , X 2 , Θ and Θ ′ be independent non-negative random variables. The residual life of X i at random time Θ , that is, X i Θ = X i − Θ ∣ X i > Θ is considered. Some sufficient conditions which lead to the likelihood ratio ordering, the failure rate ordering, the reverse failure rate ordering and the mean residual life ordering between X 1 Θ and X 2 Θ are obtained and an application in queuing theory is explained. A set of conditions which lead to the same stochastic orderings between X 1 Θ and X 1 Θ ′ are also derived. Ausführliche Beschreibung