On Construction of Bernstein-Bézier Type Bivariate Archimedean Copula

Abstract

In this paper, a new class of bivariate multi-parameter Archimedean copula based on Kendall distribution using Bernstein-Bézier polynomials is introduced. The new class copula has flexible dependence properties depending on the polynomial degree and the control points. Some dependence characteristics such as Kendall’s tau, upper tail and lower tail dependence of the new Archimedean copula class are derived. The simulation procedure based on these desired dependence characteristics is presented. Also, a parameter estimation process based on minimum Cramér-von-Mises distance is also given and its estimation performance is investigated through Monte Carlo simulation study.