Singularity aspects of Archimedean copulas

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Fernandez Sanchez, Juan¹  Trutschnig, Wolfgang² 

[1] Univ Almeria, Grp Invest Anal Matemat, La Canada De San Urbano, Almeria, Spain

[2] Salzburg Univ, Dept Math, A-5020 Salzburg, Austria

关键词: Copula;    Doubly stochastic measure;    Singular function;    Markov kernel;    Convex function;   

DOI  :  10.1016/j.jmaa.2015.06.036

来源: Elsevier

【 摘 要 】

Calculating Markov kernels of two-dimensional Archimedean copulas allows for very simple and elegant alternative derivations of various important formulas including Kendall's distribution function and the measures of the level curves. More importantly, using Markov kernels we prove the existence of singular Archimedean copulas A(phi), with full support of the following two types: (i) All conditional distribution functions y bar right arrow F-x(A phi)(y) are discrete and strictly increasing; (ii) all conditional distribution functions y bar right arrow F-x(A phi) (y) are continuous, strictly increasing and have derivative zero almost everywhere. The results show that despite of their simple analytic form Archirnedean copulas can exhibit surprisingly singular behavior. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free