A new method for the construction of bivariate Archimedean copulas based on the <tex>$\lambda$</tex> function
A new method for the construction of bivariate Archimedean copulas based on the <tex>$\lambda$</tex> function
Faculty of Applied Economics

article

2011
New York, N.Y.
, 2011

Economics

Mathematics

Communications in statistics : theory and methods. - New York, N.Y.

40(2011)
:15
, p. 2670-2679

0361-0926

000290406700004

E

English (eng)

University of Antwerp

We introduce and discuss a general method for constructing bivariate Archimedean copula families. The central item in our method is the function [image omitted] (t ∈ [0, 1]), where ϕ is the generator of the Archimedean copula. The construction of new copulas by means of λ has several advantages. The most important one is the straightforward relationship between the λ function and Kendall's τ and the coefficients of upper and lower tail dependence λL and λU, as defined in Joe (1997), which makes it possible to use these quantities as copula parameters and to control them independently of each other. Furthermore, the λ-method allows to construct multi-parameter families in a clear and organized way. The methodology is explained and illustrated by two- and three-parameter copula families.

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