Geodesic
Constructing families of symmetric dependence functions
Kybernetika, Tome 48 (2012) no. 5, pp. 977-987 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 62H20
Keywords: archimax copula; copula; dependence function; generator of a dependence function 
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     title = {Constructing families of symmetric dependence functions},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a10/}
}
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Wysocki, Włodzimierz. Constructing families of symmetric dependence functions. Kybernetika, Tome 48 (2012) no. 5, pp. 977-987. http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a10/

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