Quasi-copulas as linear combinations of copulas

被引：3
作者：
Dolinar, Gregor [1 ,2 ]
Kuzma, Bojan [2 ,3 ]
Stopar, Nik [2 ,4 ]
机构：
[1] Univ Ljubljana, Fac Elect Engn, Ljubljana, Slovenia
[2] Inst Math Phys & Mech, Ljubljana, Slovenia
[3] Univ Primorska, Fac Math, Nat Sci & Informat Technol, Koper, Slovenia
[4] Univ Ljubljana, Fac Civil & Geodet Engn, Ljubljana, Slovenia
来源：
FUZZY SETS AND SYSTEMS | 2024年 / 477卷
关键词：
Quasi-copula; Copula; Linear combination; Affine combination; Minkowski norm; BOUNDS;
D O I：
10.1016/j.fss.2023.108821
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We prove that every quasi-copula can be written as a uniformly converging infinite sum of multiples of copulas. Furthermore, we characterize those quasi-copulas which can be written as a finite sum of multiples of copulas, i.e., that are a linear combination of two copulas. This generalizes a recent result of Fernandez-Sanchez, Quesada-Molina, and ubeda-Flores who considered linear combinations of discrete copulas.
引用
收藏
页数：15
相关论文
共 24 条
[1]   ON THE CHARACTERIZATION OF A CLASS OF BINARY OPERATIONS ON DISTRIBUTION-FUNCTIONS [J].
ALSINA, C ;
NELSEN, RB ;
SCHWEIZER, B .
STATISTICS & PROBABILITY LETTERS, 1993, 17 (02) :85-89
[2]   A hitchhiker's guide to quasi-copulas [J].
Arias-Garcia, J. J. ;
Mesiar, R. ;
DeBaets, B. .
FUZZY SETS AND SYSTEMS, 2020, 393 :1-28
[3]   The unwalked path between quasi-copulas and copulas: Stepping stones in higher dimensions [J].
Arias-Garcia, J. J. ;
Mesiar, R. ;
De Baets, B. .
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING, 2017, 80 :89-99
[4]  
Darsow W.F., 1995, INT J MATH MATH SCI, V18, P417
[5]   COPULAS AND MARKOV-PROCESSES [J].
DARSOW, WF ;
NGUYEN, B ;
OLSEN, ET .
ILLINOIS JOURNAL OF MATHEMATICS, 1992, 36 (04) :600-642
[6]   Binary survival aggregation functions [J].
De Baets, B. ;
De Meyer, H. ;
Mesiar, R. .
FUZZY SETS AND SYSTEMS, 2012, 191 :83-102
[7]  
Durante F., 2016, Principles of Copula Theory
[8]   Baire category results for quasi-copulas [J].
Durante, Fabrizio ;
Fernandez-Sanchez, Juan ;
Trutschnig, Wolfgang .
DEPENDENCE MODELING, 2016, 4 (01) :215-223
[9]   New results on discrete copulas and quasi-copulas [J].
Fernandez-Sanchez, Juan ;
Juan Quesada-Molina, Jose ;
Ubeda-Flores, Manuel .
FUZZY SETS AND SYSTEMS, 2021, 415 (415) :89-98
[10]   Multivariate copulas, quasi-copulas and lattices [J].
Fernandez-Sanchez, Juan ;
Nelsen, Roger B. ;
Ubeda-Flores, Manuel .
STATISTICS & PROBABILITY LETTERS, 2011, 81 (09) :1365-1369
123