Abstract
In this article, we introduce a novel Archimedean copula constructed from a unique strict generator function. It can be described as a two-parameter unification of the well-established Gumbel-Barnett and Joe copulas. The first part is devoted to its formulation, as well as those of the corresponding density, the conditional copula, and the Kendall distribution function. Additionally, graphical representations are included to elucidate their shape behavior under various parameter configurations. In a second part, we examine some of its notable properties, with emphasis on correlation characteristics. Practical applications are discussed in the last part. In particular, we employ the maximum likelihood estimation method to determine the unknown parameters involved based on data and conduct a simulation study to demonstrate the effectiveness of this approach. Additionally, we analyze a dataset to provide practical illustrations of copula behavior and potential.
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