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Directionally Convex Comparison of Correlated First Passage Times

Author

Listed:
  • Haijun Li

    (Washington State University)

  • Susan H. Xu

    (Pennsylvania State University)

Abstract

Many important classes of multivariate distributions arising from reliability modeling are the distributions of correlated first passage times of certain multivariate point processes. In this paper, we obtain results that compare variability and dependence structure of these correlated first passage times, in the sense of directionally convex ordering. Under certain conditions, we also obtain some easily computable distributional bounds for the first passage times whose joint distributions can not be expressed explicitly.

Suggested Citation

  • Haijun Li & Susan H. Xu, 2001. "Directionally Convex Comparison of Correlated First Passage Times," Methodology and Computing in Applied Probability, Springer, vol. 3(4), pages 365-378, December.
    • Handle: RePEc:spr:metcap:v:3:y:2001:i:4:d:10.1023_a:1015412103008
    DOI: 10.1023/A:1015412103008
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    References listed on IDEAS

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    1. Pellerey, Franco, 1999. "Stochastic Comparisons for Multivariate Shock Models," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 42-55, October.
    2. Moshe Shaked & J. Shanthikumar, 1990. "Parametric stochastic convexity and concavity of stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(3), pages 509-531, September.
    3. V. G. Kulkarni, 1989. "A New Class of Multivariate Phase Type Distributions," Operations Research, INFORMS, vol. 37(1), pages 151-158, February.
    4. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    5. Susan H. Xu & Haijun Li, 2000. "Majorization of Weighted Trees: A New Tool to Study Correlated Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 298-323, May.
    6. David Assaf & Naftali A. Langberg & Thomas H. Savits & Moshe Shaked, 1984. "Multivariate Phase-Type Distributions," Operations Research, INFORMS, vol. 32(3), pages 688-702, June.
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    Cited by:

    1. Kulik, Rafal & Szekli, Ryszard, 2005. "Dependence orderings for some functionals of multivariate point processes," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 145-173, January.

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