A study of the power-cosine copula

Author(s): Christophe Chesneau1
1Université de Caen Normandie, LMNO, Campus II, Science 3, 14032, Caen, France
Copyright © Christophe Chesneau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Copulas played a key role in numerous areas of statistics over the last few decades. In this paper, we offer a new kind of trigonometric bivariate copula based on power and cosine functions. We present it via analytical and graphical approaches. We show that it may be used to create a new bivariate normal distribution with interesting shapes. Subsequently, the simplest version of the suggested copula is highlighted. We discuss some of its relationships with the Farlie-Gumbel-Morgensten and simple polynomial-sine copulas, establish that it is a member of a well-known semi-parametric family of copulas, investigate its dependence domains, and show that it has no tail dependence.

Keywords: Copulas; Farlie-Gumbel-Morgenstern copula; Polynomial-sine copula; Normal distribution; Tail dependence.