This paper introduces a new family of bivariate copulas constructed using a unit Weibull distortion. Existing copulas play the role of the base or initial copulas that are transformed or distorted into a new family of copulas with additional parameters, allowing more flexibility and better fit to data. We present a general form for the new bivariate copula function and its conditional and density distributions. The tail behaviors are investigated and indicate the unit Weibull distortion may result in new copulas with upper tail dependence when the base copula has no upper tail dependence. The concordance ordering and Kendall’s tau are derived for the cases when the base copulas are Archimedean, such as the Clayton and Frank copulas. The Loss-ALEA data are analyzed to evaluate the performance of the proposed new families of copulas.

中文翻译：

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通过单位Weibull畸变新的双变量系脉科

本文介绍了使用单位威布尔畸变构造的一族新的双变量copulas。现有的copula扮演着基础或初始copula的角色，这些基础或初始copula被转换或变形为具有其他参数的新copula系列，从而具有更大的灵活性并更好地适合数据。我们提出了新的双变量copula函数及其条件和密度分布的一般形式。研究了尾巴行为，并表明当基础系动词不具有上尾巴依赖性时，单位威布尔畸变可能导致新的系动词具有上尾巴依赖性。对于基本系动词为阿基米德语的情况（例如Clayton和Frank系动词），推导了一致顺序和Kendall的tau。对Loss-ALEA数据进行分析，以评估拟议的新系系的性能。