Y. Miao, X. M. Qu, G. Y. Yang, “Extrema of the generalized allocation scheme based on an <nobr>$m$</nobr>-dependent sequence”, Teor. Veroyatnost. i Primenen., 2022, Volume 67, Issue 2,Pages <nobr>351

Extrema of the generalized allocation scheme based on an $m$-dependent sequence

Y. Miao^ab, X. M. Qu^a, G. Y. Yang^c

^a College of Mathematics and Information Science, Henan Normal University, Henan Province, China
^b Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, Henan Normal University, Henan Province, China
^c School of Mathematics and Statistics, Zhengzhou University, Henan Province, China

Abstract: We establish some asymptotic estimations for the extrema of the generalized allocation scheme driven by $m$-dependent random variables, which extend some known results of Chuprunov and Fazekash [Discrete Math. Appl., 22 (2012), pp. 307–314] from the independent case to the $m$-dependent case.

Keywords: extrema, generalized allocation scheme, limit theorems, $m$-dependent random variables.

Received: 03.04.2020
Revised: 25.01.2022
Accepted: 29.12.2021

DOI: 10.4213/tvp5407