On copulas with a trapezoid support

Abstract

A family of bivariate copulas given by: for v+2u<2v+2u\lt 2, C(u,v)=F(2F−1(v∕2)+F−1(u))C\left(u,v)=F\left(2{F}^{-1}\left(v/2)+{F}^{-1}\left(u)), where FF is a strictly increasing cumulative distribution function of a symmetric, continuous random variable, and for v+2u≥2v+2u\ge 2, C(u,v)=u+v−1C\left(u,v)=u+v-1, is introduced. The basic properties and necessary conditions for absolute continuity of CC are discussed. Several examples are provided.

Keywords

• copulas
• tail dependence function
• kendall τ
• spearman ρ
• absolute continuity
• 62h05