A Note on a New Bivariate Copula Defined with a Piecewise Generator Function

Document Type : Original Article

Authors
1 Department of Mathematics, Universit\'e de Caen-Normandie, Caen, France.
2 Department of Industrial Engineering, Munzur University, Tunceli, Turkey.
10.22034/jirss.2025.2048996.1089
Abstract
Copulas are essential probability tools for characterizing the joint distribution of random variables. In this article, we contribute to the topic by studying special bivariate copulas. They have the property of being defined with piecewise components and are designed for the analysis of data that have dependence structures with distinct substructures in square zones. The theoretical properties of the copulas are studied, with emphasis on their mathematical validity and some dependence measures. In particular, it is shown that the Kendall tau coefficient has a simple expression that is governed by several parameters, demonstrating the flexibility of the approach. In addition, a real data example is provided to demonstrate the applicability of the copulas. Fair comparisons with other standard copulas motivate their use in other practical scenarios.
Keywords
Subjects

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Volume 23, Issue 2
December 2024
Pages 137-150

  • Receive Date 25 December 2024
  • Revise Date 21 March 2025
  • Accept Date 17 April 2025