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
Copyright Status
Unknown
Socpus ID
6444244783 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/6444244783
STARS Citation
Wang, Nan and Liu, Wei, "Expansions For The Distributions Of Some Normalized Summations Of Random Numbers Of I.I.D. Random Variables" (2002). Scopus Export 2000s. 2514.
https://stars.library.ucf.edu/scopus2000/2514