Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-06T10:17:58.841Z Has data issue: false hasContentIssue false
  • English
  • Français

On unbounded hazard rates for smoothed perturbation analysis

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Michael C. Fu  and
Jian-Qiang Hu
Michael C. Fu*
Affiliation:
University of Maryland
Jian-Qiang Hu*
Affiliation:
Boston University
*
∗Postal address: College of Business and Management, University of Maryland, College Park, MD 20742, USA.
∗∗Postal address: Department of Manufacturing Engineering, Boston University, 44 Cummington Street, Boston, MA 02215, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

Many applications of smoothed perturbation analysis lead to estimators with hazard rate functions of underlying distributions. A key assumption used in proving unbiasedness of the resulting estimator is that the hazard rate function be bounded, a restrictive assumption which excludes all distributions with finite support. Here, we prove through a simple example that this assumption can in fact be removed.

Keywords

DERIVATIVE ESTIMATIONHAZARD RATE

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 659 - 667
Copyright
Copyright © Applied Probability Trust 1995 

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.)

References

Fu, M. C. and Hu, J. Q. (1991) On choosing the characterization for smoothed perturbation analysis. IEEE Trans. Autom. Control 36, 1331–1336.CrossRefGoogle Scholar
Fu, M. C. and Hu, J. Q. (1992) Extensions and generalizations of smoothed perturbation analysis in a generalized semi-Markov process framework. IEEE Trans. Autom. Control 37, 1483–1500.CrossRefGoogle Scholar
Fu, M. C. and Hu, J. Q. (1995) Addendum to ‘Extensions and generalizations of smoothed perturbation analysis in a generalized semi-Markov process framework’. IEEE Trans. Autom. Control 40, to appear.CrossRefGoogle Scholar
Glasserman, P. (1991) Gradient Estimation Via Perturbation Analysis. Kluwer, Dordrecht.Google Scholar
Glasserman, P. and Gong, W. B. (1990) Smoothed perturbation analysis for a class of discrete event systems. IEEE Trans. Autom. Control 35, 1218–1230.CrossRefGoogle Scholar
Gong, W. B. and Ho, Y. C. (1987) Smoothed perturbation analysis of discrete-event dynamic systems. IEEE Trans. Autom. Control 32, 858–867.CrossRefGoogle Scholar
Ho, Y. C. and Cao, X. R. (1991) Discrete Event Dynamic Systems and Perturbation Analysis. Kluwer, Dordrecht.CrossRefGoogle Scholar
Papoulis, A. (1991) Probability, Random Variables, and Stochastic Processes, 3rd edn. McGraw-Hill, New York.Google Scholar
Wardi, Y., Gong, W. B., Cassandras, C. G. and Kallmes, M. H. (1992) Smothed perturbation analysis for a class of piecewise constant sample performance functions. Discrete Event Dynamic Systems: Theory and Applications 1, 393–414.Google Scholar
Weber, R. R. (1983) A note on waiting times in single server queues. Operai Res. 31, 950–951.CrossRefGoogle Scholar
Whittle, P. (1992) Probability via Expectation, 3rd edn. Springer-Verlag, New York.CrossRefGoogle Scholar
Zazanis, M. and Suri, R. (1986) Perturbation analysis for the GI/G/1 queue. Technical Report, IE/MS Department, Northwestern University.Google Scholar