Abstract

This article shows how multivariate elliptically contoured (EC) distributions, parameterized according to the mean vector and covariance matrix, can be built from univariate standard symmetric distributions. The obtained distributions are referred to as moment-parameterized EC (MEC) herein. As a further novelty, the article shows how to polynomially reshape MEC distributions and obtain distributions, called leptokurtic MEC (LMEC), having probability density functions characterized by a further parameter expressing their excess kurtosis with respect to the parent MEC distributions. Two estimation methods are discussed: the method of moments and the maximum likelihood. For illustrative purposes, normal, Laplace, and logistic univariate densities are considered to build MEC and LMEC models. An application to financial returns of a set of European stock indexes is finally presented.

摘要

本文展示了如何根据单变量标准对称分布构建根据均值向量和协方差矩阵参数化的多变量椭圆轮廓 (EC) 分布。获得的分布在本文中称为矩参数化 EC (MEC)。作为另一个新颖之处，该文章展示了如何对 MEC 分布进行多项式重构并获得称为细峰 MEC (LMEC) 的分布，该分布具有概率密度函数，其特征在于另一个参数表示它们相对于父 MEC 分布的过度峰度。讨论了两种估计方法：矩法和最大似然法。出于说明目的，考虑了正态、拉普拉斯和逻辑单变量密度来构建 MEC 和 LMEC 模型。