L_p-norm spherical copulas

06/21/2022

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by   Carole Bernard, et al.

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In this paper we study L_p-norm spherical copulas for arbitrary p ∈ [1,∞] 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.