The preservation of likelihood ratio ordering under convolution

Jevaveerasingam Shanthikumar and David Yao

Stochastic Processes and their Applications, 1986, vol. 23, issue 2, 259-267

Abstract: 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.

Keywords: shifted; likelihood; ratio; ordering; *; log-concavity; *; queueing; networks; *; total; positivity; *; conditional; stochastic; order (search for similar items in EconPapers)
Date: 1986
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Citations: View citations in EconPapers (11)

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