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978-3-8439-1585-4, Reihe Mathematik
Singular Mixture Copulas - A Geometric Method of Constructing Copulas
125 Seiten, Dissertation Carl von Ossietzky Universität Oldenburg (2014), Softcover, B5
Copulas are an important and versatile tool for modeling stochastic dependence. To cover a wide range of dependence scenarios it is essential to have several families of copulas at one's disposal.
In this thesis we present and study a new family of copulas - Singular Mixture Copulas. These copulas are the convex sums of specific singular copulas. We intensively study both copula families as well as some extensions to Singular Mixture Copulas. We particularly look at their dependence behavior.
We also study the presented copula families in a trivariate setting. To this end, we consider a trivariate random vector where two of the bivariate marginal distributions are given by either the singular copulas mentioned above or by Singular Mixture Copulas. Due to the specific construction it is possible to determine the third bivariate marginal distribution. We discuss several dependence structures and their influence on the joint distributions.