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VARIANCE BOUNDS UNDER A HAZARD RATE CONSTRAINT

Published online by Cambridge University Press:  20 December 2013

Mark Brown
Mark Brown*
Affiliation:
Department of Mathematics, The City College, CUNY E-mail: [email protected]
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Abstract

Consider an absolutely continuous distribution on [0, ∞) with known mean μ, and hazard rate function, h satisfying, 0<a≤h(t)≤b<∞, for almost all t≥0. We derive the sharp range for σ2, under these constraints.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 2 , April 2014 , pp. 203 - 208
Copyright
Copyright © Cambridge University Press 2013 

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References

1.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing: probability models, New York: Holt, Rhinehart and Winston.Google Scholar
2.Bremaud, P. (1981). Point processes and queues: martingale dynamics New York: Springer-Verlag.CrossRefGoogle Scholar
3.Brown, M. & Kemperman, J.H.B. (2009). Sharp Two-Sided bounds for distributions under a hazard rate constraint. Probability in the Engineering and Informational Sciences 23: 31–36.Google Scholar
4.Feller, W. (1966). An introduction to probability theory and its applications, Vol II. New York: John Wiley and Sons.Google Scholar
5.Marshall, A.W., & Olkin, I. (2007). Life distributions. Structure of Nonparametric, Semiparametric and Parametric Families, New York: Springer.Google Scholar