Author(s)

Min Tsao

.

We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence X_n. 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 X_n. 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 X_n.

Asymptotic Expansion; Asymptotic Normal Sequence; Edgeworth Expansion; Saddlepoint Expansion; Saddlepoints Expansion; Hermite Polynomials

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.