On the relationship between modular functions and copulas

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F15%3AA1601E6E" target="_blank" >RIV/61988987:17610/15:A1601E6E - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On the relationship between modular functions and copulas
Original language description
Copulas are nothing else but supermodular functions with absorbing element 0 and neutral element 1. Although a copula C cannot be modular on the unit square itself, it is effectively so on every rectangle with zero C-volume. In this paper, we show that an appropriate modular function on the unit square can be transformed into a copula by performing a simple truncation operation (either from below or above to ensure the compatibility with the Fréchet-Hoeffding bounds). Modular functions on the unit square admit an additive representation in terms of two univariate functions. We specifically focus on cases where these univariate functions are sections (horizontal, vertical, diagonal) of a given copula. Ample illustrations are provided.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: IT4Innovations Centre of Excellence</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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