Mean and variance of balanced Pólya urns

Abstract

It is well known that in a small Pólya urn, i.e., an urn where second largest real part of an eigenvalue is at most half the largest eigenvalue, the distribution of the numbers of balls of different colours in the urn is asymptotically normal under weak additional conditions. We consider the balanced case, and then give asymptotics of the mean and the covariance matrix, showing that after appropriate normalization, the mean and covariance matrix converge to the mean and variance of the limiting normal distribution.

24 pages

References in corpus (3)

• Analytic urns
• Asymptotics in randomized urn models
• Asymptotic theorems of sequential estimation-adjusted urn models

Cited by in corpus (1)

• Degrees in random $m$-ary hooking networks