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On the Spectrum of Asymptotic Expansions for an Asymptotic Normal Sequence

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DOI: 10.4236/ojs.2012.21010    3,306 Downloads   5,471 Views  
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We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence Xn. Members of the family are indexed by a parameter τ with an interval domain which we refer to as the spectrum of the family. The spectrum provides a unified view of known expansions for the density of Xn. It also provides a means to explore for new expansions. We discuss such applications of the spectrum through that of a sample mean and a standardized mean. We also discuss a related expansion for the cumulative distribution function of Xn.

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The authors declare no conflicts of interest.

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M. Tsao, "On the Spectrum of Asymptotic Expansions for an Asymptotic Normal Sequence," Open Journal of Statistics, Vol. 2 No. 1, 2012, pp. 98-105. doi: 10.4236/ojs.2012.21010.


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