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Keywords:
archimax copula; copula; dependence function; generator of a dependence function
archimax copula; copula; dependence function; generator of a dependence function
Summary:
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.
References:
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