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

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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 fiexibility of the new copula for negative association.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalDependence Modeling
Volume6
Issue number1
DOIs
StatePublished - 2018

Keywords

  • Archimedean copula
  • Complete monotonicity
  • Coverage probability
  • D-monotonicity
  • Kendall's distribution function
  • Kendall's tau

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