Sharp Bounds for Exponential Approximations of NWUE Distributions

被引：1
|
作者：
Brown, Mark [1 ]
Li, Shuangning [2 ]
机构：
[1] Columbia Univ, Dept Stat, New York, NY 10027 USA
[2] Stanford Univ, Stanford, CA 94305 USA
来源：
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2018年 / 20卷 / 03期
关键词：
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;
D O I：
10.1007/s11009-017-9596-x
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
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页码：875 / 896
页数：22
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