On some limit properties for the power series distribution
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Yu Miao
,
Yanyan Tang
Abstract
In the present paper, we consider random variables with the power series distribution which is often used in the study of the generalized allocation scheme. We establish some asymptotic properties which include law of large numbers, moderate deviation principle, almost sure central limit theorem and the rate of convergence in the local limit theorem. These results supplements results obtained by A. V. Kolchin.
Note: Originally published in Diskretnaya Matematika (2022) 34,№1, 88–102 (in Russian).
Acknowledgment
The authors are very grateful to the referee for his/her careful reading and helpful comments which improved the presentation of this paper.
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Funding: This work is supported by NSFC (11971154) and the Foundation of Young Scholar of the Educational Department of Henan province grant 2019GGJS012.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Diagnostic tests for discrete functions defined on rings
- New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk
- On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions
- On some limit properties for the power series distribution
- Estimates of lengths of shortest nonzero vectors in some lattices. I
Artikel in diesem Heft
- Frontmatter
- Diagnostic tests for discrete functions defined on rings
- New lower bound for the minimal number of edges of simple uniform hypergraph without the property Bk
- On some invariants under the action of an extension of GA(n, 2) on the set of Boolean functions
- On some limit properties for the power series distribution
- Estimates of lengths of shortest nonzero vectors in some lattices. I
