Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes | Sciact - Система учета научной деятельности ИМ СО РАН

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

Журнал

Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304

Вых. Данные

Год: 2023, Том: 20, Номер: 2, Страницы: 913-922 Страниц : 10 DOI: 10.33048/semi.2023.20.055

Ключевые слова

Zipf's law, weak convergence, Gaussian process, statistical test

Авторы

Chebunin M.G. ^1,2 , Kovalevskii A.P. ^2,3,4

Организации

1	Karlsruhe Institute of Technology
2	Novosibirsk State Technical University
3	Sobolev Institute of Mathematics
4	Novosibirsk State University

Информация о финансировании (1)

Математический центр в Академгородке

075-15-2022-282

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.

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

Поступила в редакцию:	1 нояб. 2022 г.
Опубликована в печати:	12 нояб. 2023 г.
Опубликована online:	12 нояб. 2023 г.

Web of science:	WOS:001102172500001
Scopus:	2-s2.0-85177554186

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