Abstract

Closed-form expressions for the expected logarithm and for
arbitrary negative integer moments of a noncentral
χ^2-distributed random variable are presented in the cases of
both even and odd degrees of freedom. Moreover, some basic
properties of these expectations are derived and tight upper and
lower bounds on them are proposed.

Keywords

Central χ^2 distribution, chi-squared distribution, expected
logarithm, exponential distribution, negative integer moments,
noncentral χ^2 distribution, squared Rayleigh distribution,
squared Rice distribution.

-||-   _|_ _|_     /    __|__   Stefan M. Moser
[-]     --__|__   /__\    /__   Senior Scientist, ETH Zurich, Switzerland
_|_     -- --|-    _     /  /   Adjunct Professor, National Yang Ming Chiao Tung University, Taiwan
/ \     []  \|    |_|   / \/    Web: https://moser-isi.ethz.ch/

Last modified: Wed Nov 11 13:48:35 CET 2020