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Diskretnaya Matematika, 2021, Volume 33, Issue 1, Pages 64–81
DOI: https://doi.org/10.4213/dm1632 (Mi dm1632) 		 
On a generalization of class of negative binomial distributions

A. N. Timashev
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DOI: https://doi.org/10.4213/dm1632
Abstract: A class of one-dimensional discrete power series distributions containing negative binomial distributions is considered. Properties of distributions of this class are investigated. Limit theorems generalizing similar theorems for the negative binomial distributions are proved. The proofs are based both on elementary asymptotic methods and on a modification of saddle-point method.
Keywords: negative binomial distribution, limit theorems, discrete distribution, large deviations, asymptotic methods, saddle-point method.
Received: 25.02.2020
English version:
Discrete Mathematics and Applications, 2022, Volume 32, Issue 4, Pages 247–261
DOI: https://doi.org/10.1515/dma-2022-0021
Bibliographic databases:
Document Type: Article
UDC: 519.213
Language: Russian
Citation: A. N. Timashev, “On a generalization of class of negative binomial distributions”, Diskr. Mat., 33:1 (2021), 64–81; Discrete Math. Appl., 32:4 (2022), 247–261
Citation in format AMSBIB
\Bibitem{Tim21}
\by A.~N.~Timashev
\paper On a generalization of class of negative binomial distributions
\jour Diskr. Mat.
\yr 2021
\vol 33
\issue 1
\pages 64--81
\mathnet{http://mi.mathnet.ru/dm1632}
\crossref{https://doi.org/10.4213/dm1632}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2830694}
\transl
\jour Discrete Math. Appl.
\yr 2022
\vol 32
\issue 4
\pages 247--261
\crossref{https://doi.org/10.1515/dma-2022-0021}
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