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VOL. 5 | 2009 Gaussian integrals involving absolute value functions
Wenbo V. Li, Ang Wei

## Abstract

We provide general formulas to compute the expectations of absolute value and sign of Gaussian quadratic forms, i.e. $\mathbb{E}$ |〈X, AX〉+〈b, X〉+c| and $\mathbb{E}$ sgn(〈X, AX〉+〈b, X〉+c) for centered Gaussian random vector X, fixed matrix A, vector b and constant c. Products of Gaussian quadratics are also discussed and followed with several interesting applications.

## Information

Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.60043
MathSciNet: MR2797939

Digital Object Identifier: 10.1214/09-IMSCOLL504