Local limit theorems for finite and infinite urn models

Abstract

Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.

Published in at http://dx.doi.org/10.1214/07-AOP350 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Notes on the occupancy problem with infinitely many boxes: general asymptotics and power laws
• Asymptotic laws for compositions derived from transformed subordinators
• Rounding of continuous random variables and oscillatory asymptotics
• On the variance of the number of occupied boxes

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• Monotonicity, asymptotic normality and vertex degrees in random graphs
• Weighted random generation of context-free languages: Analysis of collisions in random urn occupancy models
• Records in the Infinite Occupancy Scheme