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Expansions for the distributions of some normalized summations of random numbers of I.I.D. random variables

By Nan Wang and Wei Liu


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

Topics: QA
Year: 2002
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Provided by: e-Prints Soton
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