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Filtering equations for the conditional law of residual lifetimes from a heterogeneous population

Part of: Stochastic processes Stochastic systems and control Survival analysis and censored data Markov processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

A. Gerardi ,
F. Spizzichino  and
B. Torti
A. Gerardi*
Affiliation:
Università dell'Aquila
F. Spizzichino*
Affiliation:
Università ‘La Sapienza’
B. Torti*
Affiliation:
Università di Pavia
*
∗Postal address: Dipartimento di Ingegneria Elettrica, Università dell'Aquila
∗∗Postal address: Dipartimento di Matematica, Università di Roma ‘La Sapienza’, Piazzale Aldo Moro 2, I 00185 Roma, Italy. Email address: fabio.spizzichino@uniroma1.it
∗∗∗Postal address: Dipartimento di Matematica, Università di Pavia
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Abstract

We consider a probabilistic model of a heterogeneous population P subdivided into homogeneous sub-cohorts. A main assumption is that the frailties give rise to a discrete, exchangeable random vector. We put ourselves in the framework of stochastic filtering to derive the conditional distribution of residual lifetimes of surviving individuals, given an observed history of failures and survivals. As a main feature of our approach, this study is based on the analysis of behaviour of the vector of ‘occupation numbers’.

Keywords

Heterogeneous populationsexchangeabilityoccupation numbersstochastic filtering

MSC classification

Primary: 62N05: Reliability and life testing 93E11: Filtering
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60G35: Signal detection and filtering 60J75: Jump processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 3 , September 2000 , pp. 823 - 834
Copyright
Copyright © Applied Probability Trust 2000 

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