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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 503, Pages 45–47
DOI: https://doi.org/10.31857/S2686954322020199 (Mi danma247) 		 
MATHEMATICS

Behavior of binomial distribution near its median

N. A. Volkova, D. I. Dmitrievb, M. E. Zhukovskiia

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b ETH Zürich, ETH AI Center Zurich, Switzerland
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DOI: https://doi.org/10.31857/S2686954322020199
Abstract: We study the behavior of the cumulative distribution function of a binomial random variable with parameters $n$ and $b/(n+c)$ at the point $b-1$ for positive integers $b\le n$ and real $c\in[0,1]$. Our results can be applied directly to the well-known problem about small deviations of sums of independents random variables from their expectations. Moreover, we answer the question about the monotonicity of the Ramanujan function for the binomial distribution posed by Jogdeo and Samuels in 1968.
Keywords: binomial distribution, median, Ramanujan function, small deviations of sums of independent random variables.
Funding agency Grant number
Russian Science Foundation 21-71-10092
This work was supported by the Russian Science Foundation, project no. 21-71-10092.
Presented: V. V. Kozlov
Received: 06.01.2022
Revised: 06.01.2022
Accepted: 10.02.2022
English version:
Doklady Mathematics, 2022, Volume 105, Issue 2, Pages 89–91
DOI: https://doi.org/10.1134/S1064562422020193
Bibliographic databases:
Document Type: Article
UDC: 519.212.2
Language: Russian
Citation: N. A. Volkov, D. I. Dmitriev, M. E. Zhukovskii, “Behavior of binomial distribution near its median”, Dokl. RAN. Math. Inf. Proc. Upr., 503 (2022), 45–47; Dokl. Math., 105:2 (2022), 89–91
Citation in format AMSBIB
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\jour Dokl. Math.
\yr 2022
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\pages 89--91
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