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|Title:||Total variation error bounds for geometric approximation|
|Keywords:||Discrete equilibrium distribution|
Preferential attachment model
|Source:||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.|
|Appears in Collections:||Staff Publications|
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