Kybernetika 48 no. 5, 977-987, 2012

Constructing families of symmetric dependence functions

Włodzimierz Wysocki

Abstract:

We construct two pairs $(\A^{[1]}_{F}, \A^{[2]}_{F})$ and $(\A^{[1]}_{\psi}, \A^{[2]}_{\psi})$ of ordered parametric families of symmetric dependence functions. The families of the first pair are indexed by regular distribution functions $F$, and those of the second pair by elements $\psi$ of a specific function family $\bpsi$. We also show that all solutions of the differential equation $\frac{{\mathrm d}y}{{\mathrm d}u}=\frac{\alpha(u)}{u(1-u)}y$ for $\alpha$ in a certain function family $\balpha_{\rm s}$ are symmetric dependence functions.

Keywords:

copula, dependence function, archimax copula, generator of a dependence function

Classification:

62H20

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