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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Wang, N., Liu, W. 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, 114–124 (2002). https://doi.org/10.1023/A:1016169822552
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DOI: https://doi.org/10.1023/A:1016169822552