Polynomial bivariate copulas of degree five: characterization and some particular inequalities

Abstract Bivariate polynomial copulas of degree 5 (containing the family Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets ( , b c ), i.e., some set polynomials two variables 1: p x y ) = ax + by . The parameters yielding copula is characterized and visualized detail. Polynomial satisfying particular (in)equalities (symmetry, Schur concavity, positive negative quadrant dependence, ultramodularity) discussed characterized. Then it shown that for values several dependence (including Spearman’s rho, Kendall’s tau, Blomqvist’s beta, Gini’s gamma) lie exactly same intervals as copulas. Finally we prove these attain all possible ]?1, 1[ if arbitrary considered.