Expansions for the distributions of some normalized summations of random numbers of i.i.d. random variables

    Authors

    N. Wang;W. Liu

    Comments

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    Abbreviated Journal Title

    Ann. Inst. Stat. Math.

    Keywords

    central limit theorem; expansion of a tail probability; martingale; renewal theory; sequential analysis; stopping time; Wald's lemma; ASYMPTOTIC EXPANSIONS; Statistics & Probability

    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.

    Journal Title

    Annals of the Institute of Statistical Mathematics

    Volume

    54

    Issue/Number

    1

    Publication Date

    1-1-2002

    Document Type

    Article

    Language

    English

    First Page

    114

    Last Page

    124

    WOS Identifier

    WOS:000174797700008

    ISSN

    0020-3157

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