Ultramodularity and copulas

Ultramodular binary copulas are discussed, i.e., copulas of a random vector whose components are mutually stochastically decreasing with respect to each other. The additive generators of Archimedean ultramodular binary copulas are fully characterized. Finally, a new construction method for binary copulas based on n-ary ultramodular aggregation functions is proposed.

[1]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[2]  Radko Mesiar,et al.  Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms , 1999, Fuzzy Sets Syst..

[3]  Radko Mesiar,et al.  SEMPI, 2-INCREASING BINARY AGGREGATION OPERATORS , 2007 .

[4]  Radko Mesiar,et al.  Copulas Constructed from Horizontal Sections , 2007 .

[5]  Massimo Marinacci,et al.  Ultramodular Functions , 2005, Math. Oper. Res..

[6]  Anna Kolesárová,et al.  Associative n - dimensional copulas , 2011, Kybernetika.

[7]  Fabrizio Durante,et al.  ON THE CHARACTERIZATION OF A CLASS OF BINARY OPERATIONS ON BIVARIATE DISTRIBUTION FUNCTIONS , 2006 .

[8]  J.-L. Dortet-Bernadet,et al.  Dependence for Archimedean copulas and aging properties of their generating functions , 2004 .

[9]  Christian Genest,et al.  Spearman's ρ is larger than kendall's τ for positively dependent random variables , 1993 .

[10]  J. Kemperman.  On the FKG-inequality for measures on a partially ordered space , 1977 .

[11]  Radko Mesiar,et al.  2-Increasing binary aggregation operators , 2007, Inf. Sci..

[12]  M. Shaked.  A Family of Concepts of Dependence for Bivariate Distributions , 1977 .

[13]  Gleb Beliakov,et al.  Aggregation Functions: A Guide for Practitioners , 2007, Studies in Fuzziness and Soft Computing.

[14]  Radko Mesiar,et al.  Ultramodular aggregation functions , 2011, Inf. Sci..

[15]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[16]  Eckhard Liebscher,et al.  Construction of asymmetric multivariate copulas , 2008 .

[17]  Fabrizio Durante,et al.  Invariant dependence structure under univariate truncation , 2012 .

[18]  Henry W. Block,et al.  L-superadditive structure functions , 1989, Advances in Applied Probability.

[19]  A. H. Clifford,et al.  Naturally Totally Ordered Commutative Semigroups , 1954 .

[20]  R. Moynihan,et al.  On τT semigroups of probability distribution functions II , 1977 .

[21]  Alexander J. McNeil,et al.  Multivariate Archimedean copulas, $d$-monotone functions and $\ell_1$-norm symmetric distributions , 2009, 0908.3750.

[22]  Radko Mesiar,et al.  Flipping and cyclic shifting of binary aggregation functions , 2009, Fuzzy Sets Syst..

[23]  Fabrizio Durante,et al.  Rectangular Patchwork for Bivariate Copulas and Tail Dependence , 2009 .