Author:
Bandyopadhyay Antar,Kaur Gursharn
Abstract
Abstract
In this paper we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the de-preferential urn scheme. We establish the almost-sure limit of the random configuration for any balanced replacement matrix R. In particular, we show that the limiting configuration is uniform on the set of colours if and only if R is a doubly stochastic matrix. We further establish the almost-sure limit of the vector of colour counts and prove central limit theorems for the random configuration as well as for the colour counts.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Statistics and Probability
Cited by
4 articles.
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