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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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ABSTRACT

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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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