The Gumbel–Barnett family of bivariate distributions with given marginals, is frequently used in theory and applications. This family has been generalized in several ways. We propose and study a broad generalization by using two differentiable functions. We obtain some properties and describe particular cases.

中文翻译：

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Gumbel-Barnett 系的扩展

Gumbel-Barnett 系列具有给定边际的二元分布，经常用于理论和应用中。这个家族已经以多种方式概括。我们通过使用两个可微函数提出并研究了一个广泛的概括。我们获得了一些性质并描述了特定情况。