The preservation of likelihood ratio ordering under convolution

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Original languageEnglish
Pages (from-to)259-267
Journal / PublicationStochastic Processes and their Applications
Issue number2
Publication statusPublished - Dec 1986
Externally publishedYes


Unlike stochastic ordering (≥st), which is preserved under convolution (i.e., summation of independent random variables), so far it is only known that likelihood ratio ordering (≥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 (≥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. © 1986.

Research Area(s)

  • shifted likelihood ratio ordering * log-concavity * queueing networks * total positivity * conditional stochastic order