The central limit theorem without the condition of independence

L. Szeidl, V. M. Zolotarev

Research output: Contribution to journalArticle

Abstract

Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.

Original languageEnglish
Pages (from-to)3002-3004
Number of pages3
JournalJournal of Mathematical Sciences
Volume91
Issue number3
Publication statusPublished - 1998

Fingerprint

Random variables
Central limit theorem
Total Variation Distance
Metric
Independent Random Variables
Characteristic Function
Random variable
Converge
Necessary Conditions
Sufficient Conditions
Independence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistics and Probability

Cite this

The central limit theorem without the condition of independence. / Szeidl, L.; Zolotarev, V. M.

In: Journal of Mathematical Sciences, Vol. 91, No. 3, 1998, p. 3002-3004.

Research output: Contribution to journalArticle

@article{464a6db812594d839598a34e7610027b,
title = "The central limit theorem without the condition of independence",
abstract = "Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.",
author = "L. Szeidl and Zolotarev, {V. M.}",
year = "1998",
language = "English",
volume = "91",
pages = "3002--3004",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Science and Business Media Deutschland GmbH",
number = "3",

}

TY - JOUR

T1 - The central limit theorem without the condition of independence

AU - Szeidl, L.

AU - Zolotarev, V. M.

PY - 1998

Y1 - 1998

N2 - Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.

AB - Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.

UR - http://www.scopus.com/inward/record.url?scp=54749095995&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54749095995&partnerID=8YFLogxK

M3 - Article

VL - 91

SP - 3002

EP - 3004

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -