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Comparing first-passage times for semi-Markov skip-free processes

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  • Di Crescenzo, Antonio
  • Ricciardi, Luigi M.

Abstract

For two semi-Markov positive skip-free processes on conditions are given such that the first-passage times from the reflecting state 0 to a preassigned threshold are ordered according to Laplace and to increasing linear orderings. A comparison of first-passage times is performed via the new notion of 'dual weak likelihood ratio ordering'. An application to life times of devices subject to shocks and repairs is finally provided.

Suggested Citation

  • Di Crescenzo, Antonio & Ricciardi, Luigi M., 1996. "Comparing first-passage times for semi-Markov skip-free processes," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 247-256, October.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:3:p:247-256
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    References listed on IDEAS

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    1. Fagiuoli, E. & Pellerey, F., 1994. "Mean residual life and increasing convex comparison of shock models," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 337-345, August.
    2. David Sonderman, 1980. "Comparing Semi-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 110-119, February.
    3. Harshinder Singh, 1989. "On partial orderings of life distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(1), pages 103-110, February.
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    Cited by:

    1. L. Sacerdote & C. E. Smith, 2004. "Almost Sure Comparisons for First Passage Times of Diffusion Processes through Boundaries," Methodology and Computing in Applied Probability, Springer, vol. 6(3), pages 323-341, September.
    2. Emilio De Santis & Fabio Spizzichino, 2016. "Some Sufficient Conditions for Stochastic Comparisons Between Hitting Times for Skip-free Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1021-1034, December.
    3. Ferreira, Fátima & Pacheco, António, 2007. "Comparison of level-crossing times for Markov and semi-Markov processes," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 151-157, January.

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