Expansions for the distributions of some normalized summations of random numbers of I.I.D. random variables
Expansions for the distributions of some normalized summations of random numbers of I.I.D. random variables
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.
central limit theorem, expansion of a tail probability, martingale, renewal theory, sequential analysis, stopping time, Wald's lemma
114-124
Wang, Nan
a4a578fe-ce20-4131-b79b-e86af2826f8a
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
2002
Wang, Nan
a4a578fe-ce20-4131-b79b-e86af2826f8a
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Wang, Nan and Liu, Wei
(2002)
Expansions for the distributions of some normalized summations of random numbers of I.I.D. random variables.
Annals of the Institute of Statistical Mathematics, 54 (1), .
(doi:10.1023/A:1016169822552).
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.
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Published date: 2002
Keywords:
central limit theorem, expansion of a tail probability, martingale, renewal theory, sequential analysis, stopping time, Wald's lemma
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Statistics
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Local EPrints ID: 30109
URI: http://eprints.soton.ac.uk/id/eprint/30109
ISSN: 0020-3157
PURE UUID: 93e9af90-6be2-4a87-8f37-134f95fc9de4
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Date deposited: 10 May 2006
Last modified: 16 Mar 2024 02:42
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Author:
Nan Wang
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