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NONHOMOGENEOUS POISSON PROCESSES AND LOGCONCAVITY

Published online by Cambridge University Press:  01 July 2000

Franco Pellerey ,
Moshe Shaked  and
Joel Zinn
Franco Pellerey
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Moshe Shaked
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Joel Zinn
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
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Abstract

In this article, we identify conditions under which the epoch times and the interepoch intervals of a nonhomogeneous Poisson process have logconcave densities. The results are extended to relevation counting processes. We also study discrete-time counting processes and find conditions under which the epoch times and the interepoch intervals of these discrete-time processes have logconcave discrete probability densities. The results are interpreted in terms of minimal repair and record values. Several examples illustrate the theory.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 14 , Issue 3 , July 2000 , pp. 353 - 373
Copyright
© 2000 Cambridge University Press

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