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SHARP TWO-SIDED BOUNDS FOR DISTRIBUTIONS UNDER A HAZARD RATE CONSTRAINT

Published online by Cambridge University Press:  13 November 2008

Mark Brown  and
J. H. B. Kemperman
Mark Brown
Affiliation:
Department of Mathematics, The City College, CUNY, New York, NY E-mail: cybergarf@aol.com
J. H. B. Kemperman
Affiliation:
Department of Statistics, Rutgers University, New Brunswick, NJ
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Abstract

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Consider a continuous nonnegative random variable X with mean μ and hazard function h. Assume further that a≤h(t)≤b for all t≥0. Under these constraints, we obtain sharp two-sided bounds for $\bar{F}(t) = \hbox{Pr}(X \gt t)$. An application to birth and death processes is discussed.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 1 , January 2009 , pp. 31 - 36
Copyright
Copyright © Cambridge University Press 2009

References

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