FGM generated archimedean copulas with concave multiplicative generators

Document Type : Research Paper

Authors

1 Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Iran

2 Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

3 Department of Statistics, Faculty of Mathematical Sciences, Yazd University, Iran

Abstract

The Farlie-Gumble-Morgenstren (FGM) family  and  archimedean family are the most popular parametric families of copulas.  In the present paper, we propose an extension of archimedean copulas with concave multiplicative generators in the style of FGM family. In particular, our method allows the modelling of higher positive dependence than the other FGM extensions in the literature. The construction and characteristics of the proposed model along with some examples of parametric subfamilies are provided. A numerical study is used to illustrate the methodology.

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