Please use this identifier to cite or link to this item: https://doi.org/10.3150/11-BEJ406
Title: Total variation error bounds for geometric approximation
Authors: Peköz, E.A.
Röllin, A. 
Ross, N.
Keywords: Discrete equilibrium distribution
Geometric distribution
Preferential attachment model
Stein's method
Yaglom's theorem
Issue Date: May-2013
Citation: Peköz, E.A., Röllin, A., Ross, N. (2013-05). Total variation error bounds for geometric approximation. Bernoulli 19 (2) : 610-632. ScholarBank@NUS Repository. https://doi.org/10.3150/11-BEJ406
Abstract: We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a coupling between the original distribution and the "discrete equilibrium" distribution from renewal theory.We illustrate the approach in four non-trivial examples: the geometric sum of independent, non-negative, integer-valued random variables having common mean, the generation size of the critical Galton-Watson process conditioned on non-extinction, the in-degree of a randomly chosen node in the uniform attachment random graph model and the total degree of both a fixed and randomly chosen node in the preferential attachment random graph model. © 2013 ISI/BS.
Source Title: Bernoulli
URI: http://scholarbank.nus.edu.sg/handle/10635/105438
ISSN: 13507265
DOI: 10.3150/11-BEJ406
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