Year: 2013
Type: article
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.
Source: Bernoulli
DOI: 10.3150/11-bej406
Authors: Erol A. Peköz, Adrian Röllin, Nathan Ross
Institutions: Boston University, National University of Singapore
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2104144774