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Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes Full article

Journal Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304
Output data Year: 2023, Volume: 20, Number: 2, Pages: 913-922 Pages count : 10 DOI: 10.33048/semi.2023.20.055
Tags Zipf's law, weak convergence, Gaussian process, statistical test
Authors Chebunin M.G. 1,2 , Kovalevskii A.P. 2,3,4
Affiliations
1 Karlsruhe Institute of Technology
2 Novosibirsk State Technical University
3 Sobolev Institute of Mathematics
4 Novosibirsk State University

Funding (1)

1 Mathematical Center in Akademgorodok 075-15-2022-282

Abstract: We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an innite urn scheme. The probabilities of balls hitting the urns are assumed to satisfy the conditions of regular decrease. We prove weak convergence to a two-dimensional Gaussian process. Its covariance function depends only on exponent of regular decrease of probabilities. We obtain parameter estimates that have a normal asymototics for its joint distribution together with forward and backward processes. We use these estimates to construct statistical tests for the homogeneity of the urn scheme on the number of thrown balls.
Cite: Chebunin M.G. , Kovalevskii A.P.
Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. Т.20. №2. С.913-922. DOI: 10.33048/semi.2023.20.055 WOS Scopus
Dates:
Submitted: Nov 1, 2022
Published print: Nov 12, 2023
Published online: Nov 12, 2023
Identifiers:
Web of science: WOS:001102172500001
Scopus: 2-s2.0-85177554186
Citing: Пока нет цитирований
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