Elliptical tempered stable distribution
定义了椭圆型调和稳定分布及其copula，通过模拟和20国股市数据验证了其在刻画多元数据依赖结构上的优越性，对金融风险建模有参考价值。
Elliptical distributions are useful for modelling multivariate data, multivariate normal and Student t distributions being two special classes. In this paper, we provide a definition for the elliptical tempered stable (ETS) distribution based on its characteristic function, which involves a unique spectral measure. This definition provides a framework for creating a connection between the infinite divisible distribution (in particular the ETS distribution) with fractional calculus. In addition, a definition for the ETS copula is discussed. A simulation study shows the accuracy of this definition, in comparison to the normal copula for measuring the dependency of data. An empirical study of stock market index returns for 20 countries shows the usefulness of the theoretical results.