On Limit Theorems for the Distribution of the Maximal Element in a Sequence of Random Variables | Sciact - Система учета научной деятельности ИМ СО РАН

On Limit Theorems for the Distribution of the Maximal Element in a Sequence of Random Variables Научная публикация

Журнал

Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219

Вых. Данные

Год: 2024, Том: 69, Номер: 2, Страницы: 186–204 Страниц : 19 DOI: 10.1137/S0040585X97T99185

Ключевые слова

asymptotically invertible distribution, intermediate class, rapidly decreasing tails, slowly decreasing tails

Авторы

Borovkov A.A. ¹ , Prokopenko E.I. ¹

Организации

1	Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0010

We study the distribution of the maximal element ξn of a sequence of independent random variables ξ1, …, ξn and not only for them. The presented approach is more transparent (in our opinion) than the one used before. We consider four classes of distributions with right-unbounded supports and find limit theorems (in an explicit form) of the distribution of ξn for them. Earlier, only two classes of right-unbounded distributions were considered, and it was assumed a priori that the normalization of ξn is linear; in addition, the components of the normalization (in their explicit form) were unknown. For the two new classes, the required normalization turns our to be nonlinear. Results of this kind are also obtained for four classes of distributions with right-bounded support, which are analogues of the above four right-unbounded distributions (earlier, only the class of distributions with right-bounded support was considered). Some extensions of these results are obtained.

Borovkov A.A. , Prokopenko E.I.
On Limit Theorems for the Distribution of the Maximal Element in a Sequence of Random Variables
Theory of Probability and its Applications. 2024. V.69. N2. P.186–204. DOI: 10.1137/S0040585X97T99185 Scopus РИНЦ

Боровков А.А. , Прокопенко Е.И.
О предельных теоремах для распределения максимального элемента последовательности случайных величин
Теория вероятностей и ее применения. 2024. Т.69. №2. С.233-255. DOI: 10.4213/tvp5692 РИНЦ OpenAlex

Поступила в редакцию:	18 дек. 2023 г.
Опубликована в печати:	14 авг. 2024 г.
Опубликована online:	14 авг. 2024 г.

Scopus:	2-s2.0-85202581747
РИНЦ:	74317908

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