Title

Expansions For The Distributions Of Some Normalized Summations Of Random Numbers Of I.I.D. Random Variables

Keywords

Central limit theorem; Expansion of a tail probability; Martingale; Renewal theory; Sequential analysis; Stopping time; Wald's lemma

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.

Publication Date

7-11-2002

Publication Title

Annals of the Institute of Statistical Mathematics

Volume

54

Issue

1

Number of Pages

114-124

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1023/A:1016169822552

Socpus ID

6444244783 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/6444244783

This document is currently not available here.

Share

COinS