Various measures of dependence of a new asymmetric generalized Farlie–Gumbel–Morgenstern copulas

ABSTRACT

In this paper, we discuss an asymmetric extension of Farlie–Gumbel–Morgenstern copulas studied by several authors and obtain the range of the parameter. We derive an expression for regression function and the properties of these copulas are studied in detail. Also, explicit expressions for various measures of association are obtained. These measures are numerically compared for some particular parametric values of the copulas.

Keywords:

• Copulas
• FGM copulas
• Measures of association
• Regression dependence

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 60E05
• Secondary: 62H20, 62J05