Chesneau, Christophe; Susam, Selim Orhun

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.

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Susam, Selim Orhun

The purpose of this paper is to introduce a new estimation method for estimating the Archimedean copula dependence parameter in the non-parametric setting. The estimation of the dependence parameter has been selected as the value that minimizes the Cramer-von-Mises distance which measures the distance between Empirical Bernstein Kendall distribution function and true Kendall distribution function. AMonte Carlo study is performedto measure the performance of thenewestimator and compared to conventional estimation methods. In terms of estimation performance, simulation results show that the proposed Minumum Cramer-von-Mises estimation method has a good performance for low dependence and a small sample size when compared with the other estimation methods. The new minimum distance estimation of the dependence parameter is applied to model the dependence of two real data sets.

AtıfScopus13·WoS9·OpenAlex10

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