Local limit theorems for generalized scheme of allocation of particles into ordered cells

IF 0.3 Q4 MATHEMATICS, APPLIED

Discrete Mathematics and Applications Pub Date : 2021-08-01 DOI:10.1515/dma-2021-0026

A. N. Timashev

引用次数: 0

Abstract

Abstract A generalized scheme of allocation of n particles into ordered cells (components). Some statements containing sufficient conditions for the weak convergence of the number of components with given cardinality and of the total number of components to the negative binomial distribution as n → ∞ are presented as hypotheses. Examples supporting the validity of these statements in particular cases are considered. For some examples we prove local limit theorems for the total number of components which partially generalize known results on the convergence of this distribution to the normal law.

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广义粒子有序单元分配方案的局部极限定理

摘要一种将n个粒子分配到有序单元（组件）中的广义方案。一些含有给定基数的分量数和分量总数弱收敛于负二项分布的充分条件的语句为n→ ∞ 作为假设提出。考虑了在特定情况下支持这些陈述有效性的例子。对于一些例子，我们证明了分量总数的局部极限定理，这些定理部分地推广了关于该分布收敛到正态律的已知结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics and Applications MATHEMATICS, APPLIED-

CiteScore

0.60

自引率

20.00%

发文量

期刊介绍： The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.