Asymptotic expansions for probability distributions
type: Item
instance of: scholarly article
title: Asymptotic expansions for probability distributions
zbMATH Open document ID: 0536.60033
DOI: 10.1007/BF00966478
author: Sh. V. Yakshyavichyus
published in: Lithuanian Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: Asymptotic expansions of Grigelionis - Franken type are obtained in a local theorem for nonnegative integer-valued random variables \(X=X_{\Delta}[in\) spirit of \textit{V. A. Statulevičius}, Z. Wahrscheinlichkeitstheor. Verw. Geb. 6, 133-144 (1966; Zbl 0158.362)]. The limit distribution is Poisson [see also \textit{A. Bikelis} and \textit{A. Žemaitis}, Litov. Mat. Sb. 16, No.3, 31-50 (1976; Zbl 0353.60033)]. The factorial cumulants of \(X_{\Delta}\) satisfy the Bernstein- Statulevičius type condition. A parameter allowing to vary the form of expansion is involved.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3852119
zbMATH Keywords: Asymptotic expansions
zbMATH Keywords: nonnegative integer-valued random variables
MaRDI profile type: Publication
cites work: Q5336764
cites work: Convergent and Asymptotic Expansions for Probability Distributions
cites work: Q4085018
cites work: On large deviations
cites work: Approximation der Verteilungen von Summen unabhängiger nichtnegativer ganzzahliger Zufallsgrößen durch Poissonsche Verteilungen
full work available at URL: https://doi.org/10.1007/bf00966478
OpenAlex ID: W4241726530
description: scientific article; zbMATH DE number 3852119