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Random-allocation and urn models

Part of: Stochastic processes Physiological, cellular and medical topics

Published online by Cambridge University Press:  14 July 2016

J. Gani
J. Gani*
Affiliation:
Centre for Mathematics and Its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200, Australia. Email address: gani@maths.anu.edu.au
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Abstract

We review some urn and random-allocation models, mostly using probability generating function (PGF) methods. We begin by formulating a basic problem which can be thought of as either an urn or a random-allocation model; a PGF solution to it is outlined. When the compartments in the latter model are no longer homogeneous, the multivariate PGF can still be derived, though the algebra becomes cumbersome. Some results are given for the case where there are two types of compartment and for the case where there are two types of ball. Some comments are offered on the Frobenius–Harper property of PGFs.

Keywords

Urn modelsrandom-allocation modelsPGF methodsnonhomogeneous compartmentsnonhomogeneous balls

MSC classification

Primary: 60G20: Generalized stochastic processes 92C60: Medical epidemiology
Type
Part 6. Stochastic processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 313 - 320
Copyright
Copyright © Applied Probability Trust 2004 

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