The marginal distributions of multi-tail generalized elliptical dsitributions

Abstract

In the study of asset returns, most of empirical data show that the return distributions are not normally distributed. Moreover, the hypothesis of homogeneous tail behavior of the return distributions is also rejected. So we present the multi-tail generalized elliptical distribution that covers that inhomogeneous tail behavior. In addition, the multi-tail generalized elliptical distribution significantly outperforms the classical elliptical model by the paper of Kring et al. [2]. In this paper, we calculate (1) the marginal distribution of the multi-tail generalized elliptical distrubution and (2) that of the multi-tail t-distribution which is one of the multi-tail generalized elliptical distribution.