Copulas constructed from horizontal sections

Erich Klement; Anna Kolesárová; Radko Mesiar; Carlo Sempi

doi:10.1080/03610920701386976

Copulas constructed from horizontal sections

Erich Klement, Anna Kolesárová, Radko Mesiar, Carlo Sempi

Institute for Mathematical Methods in Medicine and Data Based Modeling

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

Abstract

In analogy with the study of copulas whose diagonal sections have been fixed, we study the set $\mathcal{C}_h$ of copulas for which a horizontal section h has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call horizontal copula. Then we find the copulas that bound both below and above the set $\mathcal{C}_h$. Finally, we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas.

Original language	English
Pages (from-to)	2901-2911
Number of pages	11
Journal	Communications in Statistics - Theory and Methods
Volume	36
DOIs	https://doi.org/10.1080/03610920701386976
Publication status	Published - 2007

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

10.1080/03610920701386976

Cite this

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AU - Mesiar, Radko

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AB - In analogy with the study of copulas whose diagonal sections have been fixed, we study the set $\mathcal{C}_h$ of copulas for which a horizontal section h has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call horizontal copula. Then we find the copulas that bound both below and above the set $\mathcal{C}_h$. Finally, we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas.

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DO - 10.1080/03610920701386976

M3 - Article

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VL - 36

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EP - 2911

JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

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