Polynomial bivariate copulas of degree five: characterization and some particular inequalities
| Autor: | Manuel Kauers, Radko Mesiar, Anna Kolesárová, Erich Peter Klement, Susanne Saminger-Platz, Adam Šeliga |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Polynomial Statistics::Theory Science (General) ultramodularity Copula (linguistics) 02 engineering and technology Bivariate analysis Statistics::Other Statistics Characterization (mathematics) polynomial inequality 01 natural sciences Combinatorics Set (abstract data type) 010104 statistics & probability Q1-390 primary 26b25 62e10 0202 electrical engineering electronic engineering information engineering QA1-939 Statistics::Methodology 0101 mathematics Mathematics Degree (graph theory) Applied Mathematics dependence parameter cylindrical algebraic decomposition Cylindrical algebraic decomposition Statistics::Computation Modeling and Simulation secondary 39b62 60e05 62h20 copula 020201 artificial intelligence & image processing Symmetry (geometry) schur concavity |
| Zdroj: | Dependence Modeling, Vol 9, Iss 1, Pp 13-42 (2021) |
| ISSN: | 2300-2298 |
| Popis: | Bivariate polynomial copulas of degree 5 (containing the family of Eyraud-Farlie-Gumbel-Morgenstern copulas) are in a one-to-one correspondence to certain real parameter triplets (a,b,c), i.e., to some set of polynomials in two variables of degree 1:p(x,y) =ax+by+c. The set of the parameters yielding a copula is characterized and visualized in detail. Polynomial copulas of degree 5 satisfying particular (in)equalities (symmetry, Schur concavity, positive and negative quadrant dependence, ultramodularity) are discussed and characterized. Then it is shown that for polynomial copulas of degree 5 the values of several dependence parameters (including Spearman’s rho, Kendall’s tau, Blomqvist’s beta, and Gini’s gamma) lie in exactly the same intervals as for the Eyraud-Farlie-Gumbel-Morgenstern copulas. Finally we prove that these dependence parameters attain all possible values in ]−1, 1[ if polynomial copulas of arbitrary degree are considered. |
| Databáze: | OpenAIRE |
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