Quasi-copulas with a given sub-diagonal section

José Juan Quesada-Molina; Susanne Saminger-Platz; Carlo Sempi

doi:10.1016/j.na.2007.11.021

Quasi-copulas with a given sub-diagonal section

José Juan Quesada-Molina, Susanne Saminger-Platz, Carlo Sempi

Institute for Mathematical Methods in Medicine and Data Based Modeling

Research output: Contribution to journal › Article › peer-review

Abstract

As is well known, the FrechetHoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-)copula Q, max{x + y -1, 0}<= Q(x, y)<= min{x, y} for all x, y from [0, 1]. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points (x0, 0) and (1, 1 - x0) for x0 from ]0, 1[. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.

Original language	English
Pages (from-to)	4654-4673
Number of pages	20
Journal	Nonlinear Analysis: Theory, Methods and Applications
Volume	69
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2007.11.021
Publication status	Published - 2008

Fields of science

101 Mathematics
101004 Biomathematics
101027 Dynamical systems
101013 Mathematical logic
101028 Mathematical modelling
101014 Numerical mathematics
101020 Technical mathematics
101024 Probability theory
102001 Artificial intelligence
102003 Image processing
102009 Computer simulation
102019 Machine learning
102023 Supercomputing
202027 Mechatronics
206001 Biomedical engineering
206003 Medical physics
102035 Data science

Access to Document

10.1016/j.na.2007.11.021

Cite this

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title = "Quasi-copulas with a given sub-diagonal section",

abstract = "As is well known, the FrechetHoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-)copula Q, max\{x + y -1, 0\}<= Q(x, y)<= min\{x, y\} for all x, y from [0, 1]. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points (x0, 0) and (1, 1 - x0) for x0 from ]0, 1[. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.",

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year = "2008",

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language = "English",

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AU - Quesada-Molina, José Juan

AU - Saminger-Platz, Susanne

AU - Sempi, Carlo

PY - 2008

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N2 - As is well known, the FrechetHoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-)copula Q, max{x + y -1, 0}<= Q(x, y)<= min{x, y} for all x, y from [0, 1]. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points (x0, 0) and (1, 1 - x0) for x0 from ]0, 1[. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.

AB - As is well known, the FrechetHoeffding bounds are the best possible for both copulas and quasi-copulas: for every (quasi-)copula Q, max{x + y -1, 0}<= Q(x, y)<= min{x, y} for all x, y from [0, 1]. Sharper bounds hold when the (quasi-)copulas take prescribed values, e.g., along their diagonal or horizontal resp. vertical sections. Here we pursue two goals: first, we investigate construction methods for (quasi-)copulas with a given sub-diagonal section, i.e., with prescribed values along the straight line segment joining the points (x0, 0) and (1, 1 - x0) for x0 from ]0, 1[. Then, we determine the best-possible bounds for sets of quasi-copulas with a given sub-diagonal section.

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DO - 10.1016/j.na.2007.11.021

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