Matrix representation of meet-irreducible discrete copulas

摘要

Following Aguilo-Suner-Torrens (2008), Kolesarova-Mesiar-Mordelova-Sempi (2006) and Mayor-Suner-Torrens (2005), we continue to develop a theory of matrix representation for discrete copulas. To be more precise, we give characterizations of meet-irreducible discrete copulas from an order-theoretical aspect: we show that the set of all irreducible discrete copulas is a lattice in analogy with Nelsen and Ubeda-Flores (2005). Moreover, we clarify its lattice structure related to Kendall's r and Spearman's p borrowing ideas from Coxeter groups.