A broad class of multivariate distributions for rates and proportions

Abstract

This paper introduces a general class of multivariate distributions for rates and proportions on the basis of the multivariate elliptical distribution. We derive various general properties of this multivariate distribution. The model parameters are estimated using the maximum likelihood estimation method. In particular, we have considered parameter estimation in detail for two special cases of this multivariate family, using multivariate normal kernel and multivariate Student-t kernel. Hypothesis testing inference for the correlation matrix on the basis of the likelihood ratio test statistic is also proposed. Empirical applications that employ real data are considered to illustrate the usefulness of the new class of multivariate distributions for rates and proportions in practice.