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Joint simulation of backward and forward recurrence times in a superposition of independent renewal processes

Published online by Cambridge University Press:  14 July 2016

C. Y. Teresa Lam
C. Y. Teresa Lam*
Affiliation:
University of Michigan, Ann Arbor
*
∗ Postal address: Department of Industrial and Operations Engineering, The University of Michigan, IOE Building, 1205 Beal Avenue, Ann Arbor, MI 48109–2117, USA.
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Abstract

It is shown that, in a superposition of finitely many independent renewal processes, an observation from the limiting (when t →∞) joint distribution of backward and forward recurrence times at t can be simulated by simulating an observation of the pair (UW, (1 – U)W), where U and Ware independent random variables with U ~ uniform(0, 1) and W distributed according to the limiting total life distribution of the superposition process.

Keywords

SUPERPOSITION ON RENEWAL PROCESSESLIMITING TOTAL LIFE DISTRIBUTIONSIMULATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 930 - 933
Copyright
Copyright © Applied Probability Trust 1991 

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References

Lam, C. Y. T. and Lehoczky, J. P. (1991) Superposition of renewal processes. Adv. Appl. Prob. 23, 64–85.Google Scholar
Winter, B. B. (1989) Joint simulation of backward and forward recurrence times in a renewal process. J. Appl. Prob. 26, 404–407.Google Scholar