On the area under lattice paths associated with triangular diminishing urn models
type: Item
instance of: scholarly article
title: On the area under lattice paths associated with triangular diminishing urn models
zbMATH Open document ID: 1193.60013
author: Markus Kuba
author: Alois Panholzer
published in: Advances in Applied Mathematics
publication date: 2010-04-01T00:00:00Z
review text: The paper is devoted to the analysis of the area under lattice paths, associated to a class of \(2\times 2\) triangular Pólya-Eggenberger urn models of special type. The authors derive several precise as well as asymptotic results concerning the area. Namely, they obtain a precise recursion for its positive integer moments, which in particular allows them to derive precise formulae for the mathematical expectation and the variance of the area. Moreover, this recursion yields asymptotic expansions for higher moments. As a result, the authors obtain a complete characterization of the limiting distributions of the area. The authors put a particular attention to two special cases: the pills urn model, proposed by Knuth and McCarthy, and the well-known sampling without replacement urn.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 05A16
zbMATH DE Number: 5689300
zbMATH Keywords: Pólya-Eggenberger urns models
zbMATH Keywords: lattice path
zbMATH Keywords: area distribution
zbMATH Keywords: diminishing urns
zbMATH Keywords: pills problem
zbMATH Keywords: generalized sampling urns
reviewed by: G. M. Shevchenko
MaRDI profile type: Publication
full work available at URL: j.aam.2009.09.001
OpenAlex ID: W1991113799
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DOI: 10.1016/J.AAM.2009.09.001
description: scientific article; zbMATH DE number 5689300