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A note on the exponentiality of total hazards before failure


  • Arjas, Elja
  • Haara, Pentti


It is well known that a univariate counting process with a given intensity function becomes Poisson, with unit parameter, if the original time parameter is replaced by the integrated intensity. P. A. Meyer (in Martingales (H. Dinges, Ed.), pp. 32-37. Lecture Notes in Mathematics, Vol. 190, Springer-Verlag, Berlin) showed that a similar result holds for multivariate counting processes which have continuous compensators. Even more is true in the multivariate case: If each coordinate process is transformed individually according to a convenient time change, the resulting Poisson processes become independent. Our aim is to show that the continuity assumption of the compensators can be relaxed and, when the jumps of the compensator become small, we obtain the independent Poisson processes as a limit. An application for testing goodness-of-fit in survival analysis is given.

Suggested Citation

  • Arjas, Elja & Haara, Pentti, 1988. "A note on the exponentiality of total hazards before failure," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 207-218, August.
  • Handle: RePEc:eee:jmvana:v:26:y:1988:i:2:p:207-218

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    References listed on IDEAS

    1. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    2. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
    3. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    4. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
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    Cited by:

    1. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.


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