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A class of bivariate independence copula transformations
- Source :
- Fuzzy Sets and Systems. 428:58-79
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- This paper deals with the problem of characterizing all functions f : [ 0 , 1 ] → R + such that C f ( x , y ) = x y f ( ( 1 − x ) ( 1 − y ) ) , x , y ∈ [ 0 , 1 ] is a bivariate copula. We provide a complete characterization for the two cases: (i) when C f is, in addition, totally positive of order 2 (TP2) and (ii) when f is twice continuously differentiable. In general, the function f need only be twice differentiable Lebesgue almost everywhere as shown by investigating necessary conditions for C f to be a copula. The paper also contains numerous examples illustrating obtained results and connections to known facts from the literature. Moreover, several properties of such copulas are described.
- Subjects :
- 0209 industrial biotechnology
Logic
Copula (linguistics)
02 engineering and technology
Bivariate analysis
Function (mathematics)
Characterization (mathematics)
Lebesgue integration
Combinatorics
symbols.namesake
020901 industrial engineering & automation
Artificial Intelligence
0202 electrical engineering, electronic engineering, information engineering
symbols
Order (group theory)
020201 artificial intelligence & image processing
Almost everywhere
Differentiable function
Mathematics
Subjects
Details
- ISSN :
- 01650114
- Volume :
- 428
- Database :
- OpenAIRE
- Journal :
- Fuzzy Sets and Systems
- Accession number :
- edsair.doi...........4caae44d3711b6ead1ca7ac669ebb18f