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Competing risks and independent minima: a marked point process approach

Published online by Cambridge University Press:  01 July 2016

Elja Arjas  and
Priscilla Greenwood
Elja Arjas*
Affiliation:
University of Oulu
Priscilla Greenwood*
Affiliation:
University of British Columbia
*
∗Department of Applied Mathematics and Statistics, University of Oulu, SF-90570 Oulu 57, Finland.
∗∗Department of Mathematics, University of British Columbia, Vancouver, B.C. Canada.
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Abstract

Given an indexed family of rate functions, we construct a family of independent random variables such that their minimum and the corresponding index form a marked point having the same rates. If the rates have common discontinuities, the random variables are conditionally independent, given a random allocation of these jumps. Between any two adjacent points of a marked point process there is a similar structure. Coherent functions in system lifetime theory provide examples.

Non-identifiability of multivariate lifetime distributions from mortality data is interpreted in this context.

Keywords

COMPETING RISKSINDEPENDENT MINIMAMARKED POINT PROCESSESMARTINGALE METHODSNON-IDENTIFIABILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 4 , December 1981 , pp. 669 - 680
Copyright
Copyright © Applied Probability Trust 1981 

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