Explicit expressions for joint moments of n-dimensional elliptical distributions

by   Baishuai Zuo, et al.
McMaster University
Qufu Normal University

Inspired by Stein's lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive E[X_1^2f(𝐗)] for any measurable function f satisfying some regularity conditions. Then, by applying this result, we obtain new formulae for expectations of product of normally distributed random variables, and also present simplified expressions of E[X_1^2f(𝐗)] for multivariate Student-t, logistic and Laplace distributions.


page 1

page 2

page 3

page 4


An upper bound and a characterization for Gini's mean difference based on correlated random variables

In this paper, we obtain an upper bound for the Gini mean difference bas...

A unified treatment of characteristic functions of symmetric multivariate and related distributions

The purpose of the present paper is to give unified expressions to the c...

Modified Method of Moments for Generalized Laplace Distributions

In this short note, we demonstrate the failure of the classic method of ...

The mixability of elliptical distributions with supermodular functions

The concept of ϕ-complete mixability and ϕ-joint mixability was first in...

A unified approach to explicit formulae for the distributions of runs

Fu and Koutras (1994) studied five statistics of runs and showed explici...

Regenerative properties of the linear Hawkes process with unbounded memory

We prove regenerative properties for the linear Hawkes process under min...

Please sign up or login with your details

Forgot password? Click here to reset