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314834

On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables

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Last updated: 05 Jan 2025

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Abstract

Let {Xk, k => 1} be a sequence of i.i.d.r.v.s with common distribution function (d.f.) F. Suppose F belongs to the domain of normal attraction of a stable law  with index σ, 1 < σ  ≤ 2 and F satisfies some regularity conditions. Let Sn = X1 + ... + Xn  and g be a real differentiable function such that |g'(x) - g'(y)| ≤ L |x - y|, L>0. We give uniform rate of convergence in the Central Limit Theorem (CLT) for the sequence: ( (n^1-r) / g'(o) ) { g(sn / n) - g(0) },  n ≥ 1, g'(0) ≠ 0

DOI

10.21608/esju.1993.314834

Keywords

Central Limit Theorem, Differentiable Function, Regularity Conditions, Uniform Rates of Convergence

Authors

First Name

Prashant

Last Name

Kirkire (Baroda)

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Orcid

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Volume

37

Article Issue

1

Related Issue

43175

Issue Date

1993-06-01

Receive Date

2023-08-27

Publish Date

1993-06-01

Page Start

59

Page End

64

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_314834.html

Detail API

https://esju.journals.ekb.eg/service?article_code=314834

Order

6

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

On the Uniform Rates of Convergence in the Central Limit Theorem for Functions of the Average of I. I. D. Random Variables

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Article

Created At

28 Dec 2024