Lp-norm spherical copulas

In this paper we study L-p-norm spherical copulas for arbitrary p is an element of [1, infinity] and arbitrary dimensions. The study is motivated by a conjecture that these distributions lead to a sharp bound for the value of a certain generalized mean difference. We fully characterize conditions for existence and uniqueness of L-p-norm spherical copulas. Explicit formulas for their densities and correlation coefficients are derived and the distribution of the radial part is determined. Moreover, statistical inference and efficient simulation are considered.