The Annals of Probability

Tight Bounds on the Exponential Approximation of Some Aging Distributions

D. J. Daley

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Abstract

Tight bounds on the sup metric between the exponential distribution and new better (worse) than used in expectation (NBUE, NWUE) distributions are established in terms of the proximity of the second moments of the distributions concerned. Real variable methods are used to identify the extremal distributions that attain the bounds. Similar methods establish similar results for the harmonic NBUE and NWUE classes of distributions.

Article information

Source
Ann. Probab., Volume 16, Number 1 (1988), 414-423.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991912

Digital Object Identifier
doi:10.1214/aop/1176991912

Mathematical Reviews number (MathSciNet)
MR920282

Zentralblatt MATH identifier
0638.62016

JSTOR
links.jstor.org

Subjects
Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)

Keywords
Exponential approximations NBUE NWUE HNBUE HNWUE distributions inequalities

Citation

Daley, D. J. Tight Bounds on the Exponential Approximation of Some Aging Distributions. Ann. Probab. 16 (1988), no. 1, 414--423. doi:10.1214/aop/1176991912. https://projecteuclid.org/euclid.aop/1176991912


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