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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 |
Appears in Collections: | Staff Publications |
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