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A queueing theoretical proof of increasing property of Polya frequency functions

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  • Daduna, Hans
  • Szekli, Ryszard

Abstract

Let X1,...,Xn be independent random variables with PF2 densities and [phi] an increasing function. Then E([phi](X1,...,Xn) [Sigma]i=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.

Suggested Citation

  • Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:3:p:233-242
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    References listed on IDEAS

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    1. J. George Shanthikumar & David D. Yao, 1987. "Stochastic Monotonicity of the Queue Lengths in Closed Queueing Networks," Operations Research, INFORMS, vol. 35(4), pages 583-588, August.
    2. James R. Jackson, 1957. "Networks of Waiting Lines," Operations Research, INFORMS, vol. 5(4), pages 518-521, August.
    3. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
    4. Rajan Suri, 1985. "A Concept of Monotonicity and Its Characterization for Closed Queueing Networks," Operations Research, INFORMS, vol. 33(3), pages 606-624, June.
    5. Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, April.
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    Cited by:

    1. Bogso, Antoine Marie, 2015. "MRL order, log-concavity and an application to peacocks," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1282-1306.
    2. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    3. Sauer Cornelia & Daduna Hans, 2003. "Availability Formulas and Performance Measures for Separable Degradable Networks," Stochastics and Quality Control, De Gruyter, vol. 18(2), pages 165-194, January.

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