Constructing families of symmetric dependence functions

Wysocki, Włodzimierz

Kybernetika, Tome 48 (2012) no. 5, pp. 977-987

Résumé

We construct two pairs $(\mathscr{A}^{[1]}_{F}, \mathscr{A}^{[2]}_{F})$ and $(\mathscr{A}^{[1]}_{\psi}, \mathscr{A}^{[2]}_{\psi})$ 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 $\mathbb\psi$. 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 ${\mathbb\alpha}_{\rm s}$ are symmetric dependence functions.

Détail

Classification : 62H20
Keywords: archimax copula; copula; dependence function; generator of a dependence function