The Borel Distribution: Approximation and Concentration
Fraser Daly, Seva Shneer
TL;DR
This paper develops Stein's method tools for Borel distribution approximation and derives concentration inequalities, demonstrated through queueing theory applications, enhancing understanding of Borel distribution behavior.
Contribution
It introduces new Stein's method techniques for Borel distribution approximation and establishes concentration inequalities based on size-biased representations.
Findings
Effective approximation tools for Borel distribution using Stein's method
New concentration inequalities for Borel distribution
Application to queueing theory models
Abstract
We develop the tools necessary to use Stein's method for approximation by a Borel distribution, which we illustrate by considering the approximation of the number of customers served in the busy period of an M/G/1 queue. We further derive concentration inequalities for the Borel distribution. Both these sets of results are based on a representation for the size-biased version of a Borel random variable.
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Taxonomy
TopicsRandom Matrices and Applications · Stochastic processes and statistical mechanics · Bayesian Methods and Mixture Models