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Multivariate aging properties of epoch times of nonhomogeneous processes

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  • Belzunce, Félix
  • Mercader, José A.
  • Ruiz, José M.

Abstract

The purpose of this paper is to give conditions on the parameters of nonhomogeneous Poisson and nonhomogeneous pure birth processes, under which the corresponding random vector of the first n epoch times has some multivariate stochastic properties. These results provide an inside to understand the effect of the time over the occurrence of events in such processes. Some applications of these results are given.

Suggested Citation

  • Belzunce, Félix & Mercader, José A. & Ruiz, José M., 2003. "Multivariate aging properties of epoch times of nonhomogeneous processes," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 335-350, February.
    • Handle: RePEc:eee:jmvana:v:84:y:2003:i:2:p:335-350
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    References listed on IDEAS

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    1. 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.
    2. Henry W. Block & Thomas H. Savits, 1981. "Multivariate Classes of Life Distributions in Reliability Theory," Mathematics of Operations Research, INFORMS, vol. 6(3), pages 453-461, August.
    3. Norros, Ilkka, 1985. "Systems weakend by failures," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 181-196, September.
    4. Moshe Shaked & J. George Shanthikumar, 1986. "Multivariate Imperfect Repair," Operations Research, INFORMS, vol. 34(3), pages 437-448, June.
    5. Hu, Taizhong & Pan, Xiaoming, 1999. "Preservation of multivariate dependence under multivariate claim models," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 171-179, November.
    6. Shaked, Moshe & Shanthikumar, J. George, 1991. "Dynamic multivariate aging notions in reliability theory," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 85-97, June.
    7. Moshe Shaked & J. George Shanthikumar, 1990. "Multivariate Stochastic Orderings and Positive Dependence in Reliability Theory," Mathematics of Operations Research, INFORMS, vol. 15(3), pages 545-552, August.
    8. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    9. Albert W. Marshall & Moshe Shaked, 1986. "Multivariate New Better than Used Distributions," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 110-116, February.
    10. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
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    Cited by:

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    2. Balakrishnan, N. & Beutner, E. & Kamps, U., 2008. "Order restricted inference for sequential k-out-of-n systems," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1489-1502, August.
    3. Bezgina, E. & Burkschat, M., 2019. "On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 95-109.
    4. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    5. José Pablo Arias‐Nicolás & Félix Belzunce & Olga Núñez‐Barrera & Alfonso Suárez‐Llorens, 2009. "A multivariate IFR notion based on the multivariate dispersive ordering," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 339-358, May.
    6. Balakrishnan, N. & Kamps, U. & Kateri, M., 2009. "Minimal repair under a step-stress test," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1548-1558, July.
    7. Nuria Torrado & Rosa E. Lillo & Michael P. Wiper, 2012. "Sequential Order Statistics: Ageing and Stochastic Orderings," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 579-596, September.
    8. Maryam Esna-Ashari & Narayanaswamy Balakrishnan & Mahdi Alimohammadi, 2023. "HR and RHR orderings of generalized order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 131-148, January.

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