 Explicit characterization of moments of balanced triangular Pólya urns by an elementary approachPanpan Zhang, Chen Chen and Hosam Mahmoud Statistics & Probability Letters, 2015, vol. 96, issue C, 149-153 Abstract: Two-color triangular urn models have been investigated recently. Moments of ball counts of a particular color have been obtained exactly and asymptotically in a number of sources (Janson, 2006, Kuba and Panholzer, 2014, and Flajolet et al., 2006). Exact factorial moments are in Kuba and Panholzer (2014). While Flajolet et al. (2006) gives an exact distribution, finding the exact moments from it is daunting. The asymptotic moments in Janson (2006) are derived by heavy machinery—the limit distribution in Janson (2006) is extracted from complicated characteristic functions in the form of integrals that they themselves include functions given by complicated integrals. The methods used in most of these investigations are quite sophisticated. In this note, we characterize the exact moments via an elementary approach. The formulas for the exact moments include Stirling’s numbers of second kind and the asymptotic moments follow effortlessly. Keywords: Pólya urn; Recurrence; Random structure; Combinatorial probability; Asymptotic analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:96:y:2015:i:c:p:149-153 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spl.2014.09.016 Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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