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Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 875–896 | Cite as

Sharp Bounds for Exponential Approximations of NWUE Distributions

  • Mark Brown
  • Shuangning Li
Article
  • 55 Downloads

Abstract

Let F be an NWUE distribution with mean 1 and G be the stationary renewal distribution of F. We would expect G to converge in distribution to the unit exponential distribution as its mean goes to 1. In this paper, we derive sharp bounds for the Kolmogorov distance between G and the unit exponential distribution, as well as between G and an exponential distribution with the same mean as G. We apply the bounds to geometric convolutions and to first passage times.

Keywords

Sharp error bounds for exponential approximations One and two-sided Kolmogorov distances Equilibrium distributions Geometric convolutions First passage times in time reversible Markov chains NWUE distributions 

Mathematics Subject Classification (2010)

60E15 60J27 60K10 60K25 90B25 

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA
  2. 2.Stanford UniversityStanfordUSA

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