Abstract
The class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of d-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a hierarchical structure on Archimax copulas. Second, by itself or additionally, hierarchical frailties are introduced to extend Archimax copulas to hierarchical Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Possible extensions to nested Archimax copulas are discussed. A general formula for the density and its evaluation of Archimax copulas is also introduced.
Original language | English (US) |
---|---|
Pages (from-to) | 195-211 |
Number of pages | 17 |
Journal | JOURNAL OF MULTIVARIATE ANALYSIS |
Volume | 167 |
DOIs | |
State | Published - Sep 2018 |
Keywords
- Archimax copulas
- Hierarchical frailties
- Hierarchical stable tail dependence functions
- Nesting
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty