Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T04:04:29.970Z Has data issue: false hasContentIssue false
  • English
  • Français

Interparticle dependence in a linear death process subjected to a random environment

Published online by Cambridge University Press:  14 July 2016

Claude Lefèvre  and
György Michaletzky
Claude Lefèvre*
Affiliation:
Université de Bruxelles
György Michaletzky*
Affiliation:
University Eötvös L.
*
∗Postal address: Université Libre de Bruxelles, Institut de Statistique, C.P. 210, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
∗∗Postal address: University Eötvös L., Department of Probability Theory and Statistics, 1088 Muzeum Krt 6-8, Budapest, VIII ker, Hungary.
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently, Ball and Donnelly (1987) investigated the nature of the interparticle dependence in a death process with non-linear rates. In this note, after some remarks on their result, a similar problem is examined for a linear death process where the death rate per particle is a monotone function of the current state of a random environment. It is proved that if the exterior process involved is a homogeneous birth-and-death process valued in ℕ, then the survival times of any subset of particles are positively upper orthant dependent. A simple example shows that this property is not valid for general exterior processes.

Keywords

RISK-SHARING SYSTEMBIRTH-AND-DEATH ENVIRONMENTWEISS EPIDEMIC MODELUPPER ORTHANT DEPENDENT VARIABLESASSOCIATED VARIABLES
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 491 - 498
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research was partially supported by a grant of the Belgium F.N.R.S.

The paper was written while the authors were visting the Statistics and Applied Probability Program, University of California, Santa Barbara.

References

Ball, F. and Donnelly, P. (1987) Interparticle correlation in death processes with applications to variability in compartmental models. Adv. Appl. Prob. 19, 755–766.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing. Holt, New York.Google Scholar
Joag-Dev, K. and Proschan, F. (1983) Negative association of random variables, with applications. Ann. Statist. 11, 286–295.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Schechner, Z. (1984) A load-sharing model: the linear breakdown rule. Naval Res. Log. Quart. 31, 137–144.CrossRefGoogle Scholar
Shared, M. and Shanthikumar, J. G. (1987) Multivariate hazard rates and stochastic ordering. Adv. Appl. Prob. 19, 123–137.Google Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, 481–490.Google Scholar