Hostname: page-component-77f85d65b8-8v9h9 Total loading time: 0 Render date: 2026-03-26T18:50:47.486Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Abstract

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 . 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

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.)

Article purchase

Temporarily unavailable

References

1.Aldous, D.J. & Brown, M. (1993). Inequalities for rare events in time-reversible Markov chains. In Shaked, Moshe and Tong, Y. L.(eds), Stochastic inequalities, IMS Lecture Notes Monograph Series, pp. 1–16, Hayward, California: Institute of Mathematical Statistics.Google Scholar
2.Barlow, R.E. & Proschan, F. (1975). Statistical theory of reliability and life testing. New York: Holt Rinehart and Winston.Google Scholar
3.Keilson, J. (1979). Markov chain models: Rarity and exponentiality. New York: Springer-Verlag.CrossRefGoogle Scholar
4.Marshall, A.W. & Olkin, I. (2007). Structure of life distributions: Nonparametric, semiparametric, and parametric families. New York: Springer-Verlag.Google Scholar
5.Taylor, H.M. & Karlin, S. (1994). An introduction to stochastic modeling, rev. ed. New York: Academic Press.Google Scholar