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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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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    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. Francisco Germán Badía & Sophie Mercier & Carmen Sangüesa, 2019. "Extensions of the Generalized Pólya Process," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1057-1085, December.
    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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