Explicit formulae and implication of the expected values of some nonlinear statistics of tri-variate Gaussian variables

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We obtain explicit formulae for the expected values E{3 i=1 gi ( Xi)} of standard tri-variate Gaussian random vector X = (X1, X2, X3) over the set gi (x). {d(x), sgn(x), |x|, x} of nonlinear and linear functions. Based on the results, we also suggest corrections to long-known formulae for two incomplete moments. Applications of the formulae in practical examples are also illustrated concisely. For easy reference for the readers, the explicit formulae derived in this paper and related wellknown results are summarized in tables.
Publisher
SPRINGER HEIDELBERG
Issue Date
2020-03
Language
English
Article Type
Article
Citation

JOURNAL OF THE KOREAN STATISTICAL SOCIETY, v.49, no.1, pp.117 - 138

ISSN
1226-3192
DOI
10.1007/s42952-019-00009-9
URI
http://hdl.handle.net/10203/273940
Appears in Collection
EE-Journal Papers(저널논문)
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