Abstract Several extensions of the family of (bivariate) Eyraud-Farlie-Gumbel-Morgenstern copulas (EFGM copulas) are considered. Some of them are well-known from the literature, others have recently been suggested (copulas based on quadratic constructions, based on some forms of convexity, and polynomial copulas). For each of these extensions we analyze which properties of EFGM copulas are preserved (or even improved) and which are (partly) lost. Such properties can be structural (order theoretical or topological) in nature, or algebraic (symmetry or being a polynomial) or analytic (absolute continuity). Other examples are forms of convexity, quadrant dependence, and symmetry with respect to copula transformations. The last group of properties considered here is related to some dependence parameters.

中文翻译：

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扩展该族时对 EFGM copula 属性的影响

摘要 考虑了（双变量）Eyraud-Farlie-Gumbel-Morgenstern copulas（EFGM copulas）家族的几个扩展。其中一些在文献中是众所周知的，其他一些最近已经被提出（基于二次构造的联结，基于某些形式的凸性，以及多项式联结）。对于这些扩展中的每一个，我们分析 EFGM copula 的哪些属性被保留（甚至改进），哪些（部分）丢失。这些性质在本质上可以是结构的（有序理论或拓扑的），也可以是代数的（对称性或多项式）或解析的（绝对连续性）。其他示例是关于 copula 变换的凸性、象限相关性和对称性的形式。这里考虑的最后一组属性与一些依赖参数有关。