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On the Variance of the Hazard Estimator in Simulation

Published online by Cambridge University Press:  27 July 2009

Gerald J. Lieberman  and
Sheldon M. Ross
Gerald J. Lieberman
Affiliation:
Department of Operations Research Stanford University Stanford, California 94305
Sheldon M. Ross
Affiliation:
Department of Industrial Engineering and Operations Research University of California, Berkeley Berkeley, California94720
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Abstract

Suppose a discrete time Markov process is simulated so as to estimate p, the probability that it enters the set of states A before it enters the set of states B, for disjoint sets A and B. It is shown that the total hazard, which is an unbiased estimator of p, has a variance that is bounded above by p(2 – p).

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 5 , Issue 3 , July 1991 , pp. 355 - 359
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

Ross, S. (1990). Variance reduction in simulation via random hazards. Probability in the Engineering and Informational Sciences 4: 299–310.CrossRefGoogle Scholar
Ross, S. & Schechner, Z. (1985). Using simulation to estimate first passage distributions. Managemern Science 31: 224–235.CrossRefGoogle Scholar
Schechner, Z. (1982). The total hazard is exponential. Naval Research Logistics Quarterly 29: 684–690.Google Scholar