Strictly Archimedean copulas with complete association for multivariate dependence based on the Clayton family

Abstract

Abstract The family of Clayton copulas is one of the most widely used Archimedean copulas for dependency measurement. A major drawback of this copula is that when it accounts for negative dependence, the copula is nonstrict and its support is dependent on the parameter. The main motivation for this paper is to address this drawback by introducing a new two-parameter family of strict Archimedean copulas to measure exchangeable multivariate dependence. Closed-form formulas for both complete and d−monotonicity parameter regions of the generator and the copula distribution function are derived. In addition, recursive formulas for both copula and radial densities are obtained. Simulation studies are conducted to assess the performance of the maximum likelihood estimators of d−variate copula under known marginals. Furthermore, derivativefree closed-form formulas for Kendall’s distribution function are derived. A real multivariate data example is provided to illustrate the flexibility of the new copula for negative association.