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September 2015 Sharp bounds for exponential approximations under a hazard rate upper bound
Mark Brown
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J. Appl. Probab. 52(3): 841-850 (September 2015). DOI: 10.1239/jap/1445543850

Abstract

Consider an absolutely continuous distribution on [0, ∞) with finite mean μ and hazard rate function h(t) ≤ b for all t. For bμ close to 1, we would expect F to be approximately exponential. In this paper we obtain sharp bounds for the Kolmogorov distance between F and an exponential distribution with mean μ, as well as between F and an exponential distribution with failure rate b. We apply these bounds to several examples. Applications are presented to geometric convolutions, birth and death processes, first-passage times, and to decreasing mean residual life distributions.

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Mark Brown. "Sharp bounds for exponential approximations under a hazard rate upper bound." J. Appl. Probab. 52 (3) 841 - 850, September 2015. https://doi.org/10.1239/jap/1445543850

Information

Published: September 2015
First available in Project Euclid: 22 October 2015

zbMATH: 1331.60037
MathSciNet: MR3414995
Digital Object Identifier: 10.1239/jap/1445543850

Subjects:
Primary: 60E15
Secondary: 60J27, 60J80, 60K20, 90B25

Rights: Copyright © 2015 Applied Probability Trust

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Vol.52 • No. 3 • September 2015
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