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Some Reliability Applications of the Variability Ordering

Author

Listed:
  • Sheldon M. Ross

    (University of California, Berkeley, California)

  • Zvi Schechner

    (Columbia University, New York, New York)

Abstract

The random variable X is said to be more variable than Y if E [ f ( X )] ≥ E [ f ( Y )] for all increasing convex functions f . We prove a preservation property of this ordering under random sized sums, and then apply it to branching processes and shock models. We also give applications of this ordering to a population survival and to a Poisson shock model.

Suggested Citation

  • Sheldon M. Ross & Zvi Schechner, 1984. "Some Reliability Applications of the Variability Ordering," Operations Research, INFORMS, vol. 32(3), pages 679-687, June.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:3:p:679-687
    DOI: 10.1287/opre.32.3.679
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    Cited by:

    1. Mohammed Mohammed Ahmed Almazah & Badr Alnssyan & Abdul Hadi N. Ahmed & Ahmed Z. Afify, 2021. "Reliability Properties of the NDL Family of Discrete Distributions with Its Inference," Mathematics, MDPI, vol. 9(10), pages 1-17, May.
    2. Belzunce, Félix & Shaked, Moshe, 2001. "Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability theory," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 363-372, July.

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