The class of multivariate max-id copulas with $\ell_{1}$-norm symmetric exponent measure
The class of multivariate max-id copulas with $\ell_{1}$-norm symmetric exponent measure
复制标题
具有 $ell_{1}$-norm 对称指数测度的多元 max-id 联结函数类
作者：
C. Genest;J. Nešlehová;L. Rivest
著名的二元Galambos copula族的成员可以用一元Fréchet分布的封闭形式表示。这个公式可以扩展到任何维度，并可以用来定义一个全新的类别，由合适的单变量分布生成的易处理的多元copula。本文给出了Copula存在的一元分布的充分必要条件。证明了这些新的Copula函数实际上是具有1-范数对称指数测度的max-id分布的相依结构。研究了这类新的多元可交换Copula函数的基本依赖性质，并给出了一个从这类函数中的分布生成观测值的有效算法。
Members of the well-known family of bivariate Galambos copulas can be expressed in a closed form in terms of the univariate Fréchet distribution. This formula extends to any dimension and can be used to define a whole new class of tractable multivariate copulas that are generated by suitable univariate distributions. This paper gives necessary and sufficient conditions on the underlying univariate distribution which ensure that the resulting copula exists. It is also shown that these new copulas are in fact dependence structures of certain max-id distributions with `1-norm symmetric exponent measure. The basic dependence properties of this new class of multivariate exchangeable copulas is investigated, and an efficient algorithm is provided for generating observations from distributions in this class.