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A note on the exponentiality of total hazards before failure

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  • Arjas, Elja
  • Haara, Pentti

Abstract

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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    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.
    2. Clive Bowsher, 2002. "Modelling Security Market Events in Continuous Time: Intensity based, Multivariate Point Process Models," Economics Series Working Papers 2002-W22, University of Oxford, Department of Economics.
    3. Clive Bowsher, 2004. "Modelling Security Market Events in Continuous Time: Intensity Based, Multivariate Point Process Model," Economics Series Working Papers 2003-W03, University of Oxford, Department of Economics.

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