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<p>In this article, a new bivariate Clayton copula called the Generalized Bivariate Clayton (GBC) Copula is obtained. The classical one-parameter Clayton copula emerges as a special case of the Generalized Bivariate Clayton Copula. The derivation of the Generalized Bivariate Clayton Copula is motivated by a conjecture of Nelsen (1999, Example 2.14), which suggests a one-to-one correspondence between the Pareto distribution and the Clayton copula. Furthermore, it is demonstrated that the Generalized Bivariate Clayton Copula can be represented in terms of the classical Clayton copula and the product copula, both of which belong to the Archimedean family of copulas. Finally, two applications of the Generalized Bivariate Clayton Copula are presented.</p>

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A New Two Parameter Bivariate Clayton Copula with Applications in Reliability

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Agnideep Aich,
  • Ashit Baran Aich

摘要

In this article, a new bivariate Clayton copula called the Generalized Bivariate Clayton (GBC) Copula is obtained. The classical one-parameter Clayton copula emerges as a special case of the Generalized Bivariate Clayton Copula. The derivation of the Generalized Bivariate Clayton Copula is motivated by a conjecture of Nelsen (1999, Example 2.14), which suggests a one-to-one correspondence between the Pareto distribution and the Clayton copula. Furthermore, it is demonstrated that the Generalized Bivariate Clayton Copula can be represented in terms of the classical Clayton copula and the product copula, both of which belong to the Archimedean family of copulas. Finally, two applications of the Generalized Bivariate Clayton Copula are presented.