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A note on random intensities and conditional survival functions

Published online by Cambridge University Press:  14 July 2016

Anatoli Yashin  and
Elja Arjas
Anatoli Yashin*
Affiliation:
Institute of Control Sciences, Moscow
Elja Arjas*
Affiliation:
University of Oulu
*
∗ Postal address: Institute of Control Sciences, Profsojusnaya 65, Moscow, USSR.
∗∗ Postal address: Department of Applied Mathematics and Statistics, University of Oulu, Linnanmaa, 90570 Oulu, Finland.
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Abstract

Failure intensities in which the evaluation of hazard is based on the observation of an auxiliary random process have become very popular in survival analysis. While their definition is well known, either as the derivative of a conditional failure probability or in the counting process and martingale framework, their relationship to conditional survival functions does not seem to be equally well understood. This paper gives a set of necessary and sufficient conditions for the so-called exponential formula in this context.

Keywords

HAZARD RATECOUNTING PROCESSMARTINGALEEXPONENTIAL FORMULA
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 3 , September 1988 , pp. 630 - 635
Copyright
Copyright © Applied Probability Trust 1988 

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