The preservation of likelihood ratio ordering under convolution (Q1087229)

Unlike stochastic ordering \((\geq^{st})\), which is preserved under convolution (i.e., summation of independent random variables), so far it is only known that likelihood ratio ordering \((\geq^{lr})\) is preserved under convolution of log-concave \((PF_ 2)\) random variables. In this paper we define a stronger version of likelihood ratio ordering, termed shifted likelihood ratio ordering \((\geq_{\uparrow}^{lr})\) and show that it is preserved, under convolution. An application of this closure property to closed queueing network is given. Other properties of shifted likelihood ratio ordering are also discussed.