Open AccessJournal Article
Asymmetric semilinear copulas
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Two new classes are introduced, called vertical and horizontal semilinear copulas, and their corresponding class of diagonals are characterized, which are in essence asymmetric, with maximum asymmetry given by 1/16.Abstract:
We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1/16. The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of II and M.read more
Citations
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Book ChapterDOI
Copula Theory: An Introduction
Fabrizio Durante,Carlo Sempi +1 more
TL;DR: In this survey, the most important properties of copula are reviewed, several families of copulas that have appeared in the literature, and which have been applied in various fields, and several methods of constructing multivariate copulas are reviewed.
Journal ArticleDOI
Semilinear copulas
TL;DR: A family of copulas, called semilinear, is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square, and a special form of ordinal sum construction is introduced.
Book ChapterDOI
Assessing and Modeling Asymmetry in Bivariate Continuous Data
TL;DR: In this article, the authors revisited key aspects of this issue from a modeling perspective, including measures of asymmetry and rank-based estimators thereof, along with recently proposed tests of symmetry.
Journal ArticleDOI
Measures of non-exchangeability for bivariate random vectors
TL;DR: In this paper, a set of axioms for measures of non-exchangeability for bivariate vectors of continuous and identically distributed random variables are introduced, together with possible applications in statistical models based on the copula function.
Journal ArticleDOI
Bivariate copulas: Transformations, asymmetry and measures of concordance
Sebastian Fuchs,Klaus D. Schmidt +1 more
TL;DR: A group of transformations on the collection of all bivariate copulas is introduced which contains an involution which is particularly useful since it provides a criterion under which a given symmetric copula can be transformed into an asymmetric one.
References
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Book
An Introduction to Copulas
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Journal ArticleDOI
On the construction of copulas and quasi-copulas with given diagonal sections ☆
TL;DR: A method for creating new functions by joining portions of two copulas (or quasi-copulas) with a common diagonal section is studied, and a necessary and sufficient condition is found for the diagonal splice of twoCopula to be a copula.
Journal ArticleDOI
Semilinear copulas
TL;DR: A family of copulas, called semilinear, is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square, and a special form of ordinal sum construction is introduced.