On Limit Theorems for the Distribution of the Maximal Element in a Sequence of Random Variables Full article
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Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219 |
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| Output data | Year: 2024, Volume: 69, Number: 2, Pages: 186–204 Pages count : 19 DOI: 10.1137/S0040585X97T99185 | ||
| Tags | asymptotically invertible distribution, intermediate class, rapidly decreasing tails, slowly decreasing tails | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0010 |
Abstract:
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.
Cite:
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
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
Original:
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
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
Dates:
| Submitted: | Dec 18, 2023 |
| Published print: | Aug 14, 2024 |
| Published online: | Aug 14, 2024 |
Identifiers:
| Scopus: | 2-s2.0-85202581747 |
| Elibrary: | 74317908 |
Citing:
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