Title

Expansions for the distributions of some normalized summations of random numbers of i.i.d. random variables

Authors

Authors

N. Wang;W. Liu

Comments

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Abbreviated Journal Title

Ann. Inst. Stat. Math.

Keywords

central limit theorem; expansion of a tail probability; martingale; renewal theory; sequential analysis; stopping time; Wald's lemma; ASYMPTOTIC EXPANSIONS; Statistics & Probability

Abstract

The central limit theorem for a normalized summation of random number of i.i.d. random variables is well known. In this paper we improve the central limit theorem by providing a two-term expansion for the distribution when the random number is the first time that a simple random walk exceeds a given level. Some numerical evidences are provided to show that this expansion is more accurate than the simple normality approximation for a specific problem considered.

Journal Title

Annals of the Institute of Statistical Mathematics

Volume

54

Issue/Number

1

Publication Date

1-1-2002

Document Type

Article

Language

English

First Page

114

Last Page

124

WOS Identifier

WOS:000174797700008

ISSN

0020-3157

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