Sharp Bounds for Exponential Approximations of NWUE Distributions

Mark Brown () and Shuangning Li ()
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Mark Brown: Columbia University
Shuangning Li: Stanford University

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 3, 875-896

Abstract: 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; 60E15; 60J27; 60K10; 60K25; 90B25 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-017-9596-x

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