On the area under lattice paths associated with triangular diminishing urn models
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.
scientific article; zbMATH DE number 5689300
scientific article