The preservation of likelihood ratio ordering under convolution
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.
scientific article; zbMATH DE number 3988385
scientific article