Functional central limit theorems for certain statistics in an infinite urn scheme
Mikhail Chebunin, Artyom Kovalevskii
TL;DR
This paper proves functional central limit theorems for the total number of urns with at least k balls in a specific infinite urn scheme, extending understanding of its probabilistic behavior.
Contribution
It establishes new functional central limit theorems for certain statistics in an infinite urn scheme, building on Karlin's 1967 model.
Findings
Proves functional CLTs for urns with at least k balls
Extends probabilistic analysis of infinite urn schemes
Provides theoretical foundation for further statistical studies
Abstract
We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for different k.
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