Large deviations of combinatorial distributions. II: Local limit theorems
type: Item
instance of: scholarly article
title: Large deviations of combinatorial distributions. II: Local limit theorems
zbMATH Open document ID: 0954.60020
author: Hsien-Kuei Hwang
published in: The Annals of Applied Probability
publication date: 2001-01-25T00:00:00Z
review text: [For part I see ibid. 6, No. 1, 297-319 (1996; Zbl 0863.60013).] Let \(\{\Omega _n\}_{n\geq 1} \) be a sequence of random variables taking integral values and of maximal span 1 for \(n\geq n_0\); \(\mu_n={\mathbb{E}} \Omega_n\); \(\sigma_n^2=\text{ Var} \Omega_n\). The asymptotic formulas for \(\text{ Pr} \{\Omega_n=m\}\) for \(m\) lying in the interval \(\mu_n + O(\sigma_n^2)\) are obtained under conditions on the moment generating function of \(\Omega_n\). The result is derived by means of the saddlepoint method on Laplace-type integrals and may be applicable considering parameters of combinatorial structures, as well as the distribution of arithmetical functions.
reviewed by: Aleksandras Plikusas
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 05A16
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 1319848
zbMATH Keywords: lattice random variable
zbMATH Keywords: moment generating function
zbMATH Keywords: large deviations
zbMATH Keywords: local limit theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1027961038
OpenAlex ID: W2017306457
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DOI: 10.1214/AOAP/1027961038
description: scientific article; zbMATH DE number 1319848