A queueing theoretical proof of increasing property of Polya frequency functions

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Abstract

Let X1,…,Xn be independent random variables with PF2 densities and φ an increasing function. Then E(φ(X1,…,Xn)| Σi=1n X1 = s) is increasing in s, almost surely (Efron, 1965). We put this theorem into the context of queueing theory and provide an elementary proof for non-negative random variables.

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