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

被引：0

作者：

Song, Iickho ^{[1
,2
]}

Lee, Seungwon ^{[1
]}

Kim, Yun Hee ^{[3
]}

Park, So Ryoung ^{[4
]}

机构：

[1] Korea Adv Inst Sci & Technol, Sch Elect Engn, Daejeon 34141, South Korea

[2] Chongqing Univ Technol, Liangjiang Int Coll, Chongqing 401135, Peoples R China

[3] Kyung Hee Univ, Dept Elect Engn, Yongin 17104, South Korea

[4] Catholic Univ Korea, Sch Informat Commun & Elect Engn, Bucheon 14662, South Korea

来源：

JOURNAL OF THE KOREAN STATISTICAL SOCIETY | 2020年 / 49卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Absolute moment; Impulse function; Magnitude; Nonlinear function; Signum function; Tri-variate Gaussian distribution; DETECTION PERFORMANCE; MOMENTS; SIGNALS;

D O I：

10.1007/s42952-019-00009-9

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：117 / 138

页数：22