The preservation of likelihood ratio ordering under convolution

Unlike stochastic ordering ([greater-or-equal, slanted]st), which is preserved under convolution (i.e., summation of independent random variables), so far it is only known that likelihood ratio ordering ([greater-or-equal, slanted]lr) is preserved under convolution of log-concave (PF2) random variables. In this paper we define a stronger version of likelihood ratio ordering, termed shifted likelihood ratio ordering ([greater-or-equal, slanted]lr[short up arrow]) 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.