Email this article The Rate of Convergence of the Distributions of Regular Statistics Constructed from Samples with Negatively Binomially Distributed Random Sizes to the Student Distribution
- Authors: Gavrilenko S.V.1, Zubov V.N.1, Korolev V.Y.1,2
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Affiliations:
- Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
- Institute of Informatics Problems of RAS
- Issue: Vol 220, No 6 (2017)
- Pages: 701-713
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/238916
- DOI: https://doi.org/10.1007/s10958-016-3213-3
- ID: 238916
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Abstract
New estimates are obtained for the rate of convergence of the negative binomial distribution with parameters (r, p) to the gamma-distribution with parameters (r, r) when p → 0. The main result is a considerable improvement of convergence rate estimates for regular statistics constructed from samples with negatively binomially distributed random sizes to the Student distribution.
About the authors
S. V. Gavrilenko
Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Email: vkorolev@cs.msu.su
Russian Federation, Moscow
V. N. Zubov
Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Email: vkorolev@cs.msu.su
Russian Federation, Moscow
V. Yu. Korolev
Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics; Institute of Informatics Problems of RAS
Author for correspondence.
Email: vkorolev@cs.msu.su
Russian Federation, Moscow; Moscow
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