On copulas with a trapezoid support

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