On the existence of a trivariate copula with given values of a trivariate quasi-copula at several points
| Autor: | Manuel íbeda-Flores, Juan Fernández Sánchez, Bernard De Baets, Hans De Meyer |
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| Rok vydání: | 2013 |
| Předmět: |
Statistics::Theory
Transitive relation Multivariate statistics Linear programming Logic Mathematical analysis Statistics::Other Statistics Bivariate analysis Lipschitz continuity Statistics::Computation Copula (probability theory) Computer Science::Graphics Simplex algorithm Artificial Intelligence Unit cube Statistics::Methodology Applied mathematics Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 228:3-14 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2012.07.006 |
| Popis: | The existence of a (multivariate) copula with a given value of a (multivariate) quasi-copula at a single point is known. In the bivariate case, the existence of a copula with given values of a quasi-copula at two or three arbitrary points is also known. In this paper, we give an alternative proof of the existence of a trivariate copula with a given value of a trivariate quasi-copula at a single point. This proof relies on the reformulation of the existence problem as a linear programming minimization problem and its solution by means of the simplex algorithm. The same method is then used to prove the existence of a trivariate copula with given values of a trivariate quasi-copula at two arbitrary points in the unit cube. We furthermore establish a counter-example showing that the existence for given values at three points is not guaranteed. This completes the analysis of the trivariate case. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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