标题： 幂发散Copula：一类新的Archimedean Copula，具有保险应用 显示英文标题

标题： Power-divergence copulas: A new class of Archimedean copulas, with an insurance application

摘要： 本文表明，在某种特定的约定下，表征phi散度的凸函数在至少两个维度中也能生成阿基米德Copula。 作为特殊情况，我们开发了与重要的幂散度家族相关的阿基米德Copula家族，我们称之为幂散度Copula。 该家族的性质得到了广泛研究，包括绝对连续或具有奇异成分的子家族、该家族的排序、极限情况（即弗雷歇-霍夫丁下界和弗雷歇-霍夫丁上界）、肯德尔τ系数和尾部依赖系数，以及扩展到三个或更多维度的情况。 在一项说明性的应用中，幂散度Copula被用于建模丹麦火灾保险数据集。 结果表明，幂散度Copula能够很好地拟合由企业提出的两种火灾相关损失的双变量分布，而几个基准模型（一系列著名的阿基米德、极值和椭圆Copula）则不能。 显示英文摘要

摘要： This paper demonstrates that, under a particular convention, the convex functions that characterise the phi divergences also generate Archimedean copulas in at least two dimensions. As a special case, we develop the family of Archimedean copulas associated with the important family of power divergences, which we call the power-divergence copulas. The properties of the family are extensively studied, including the subfamilies that are absolutely continuous or have a singular component, the ordering of the family, limiting cases (i.e., the Frechet-Hoeffding lower bound and Frechet-Hoeffding upper bound), the Kendall's tau and tail-dependence coefficients, and cases that extend to three or more dimensions. In an illustrative application, the power-divergence copulas are used to model a Danish fire insurance dataset. It is shown that the power-divergence copulas provide an adequate fit to the bivariate distribution of two kinds of fire-related losses claimed by businesses, while several benchmarks (a suite of well known Archimedean, extreme-value, and elliptical copulas) do not.