Constructing families of symmetric dependence functions

Wysocki, Włodzimierz. "Constructing families of symmetric dependence functions." Kybernetika 48.5 (2012): 977-987. <http://eudml.org/doc/251414>.

@article{Wysocki2012,
abstract = {We construct two pairs $(\mathcal \{A\}^\{[1]\}_\{F\}, \mathcal \{A\}^\{[2]\}_\{F\})$ and $(\mathcal \{A\}^\{[1]\}_\{\psi \}, \mathcal \{A\}^\{[2]\}_\{\psi \})$ 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.},
author = {Wysocki, Włodzimierz},
journal = {Kybernetika},
keywords = {archimax copula; copula; dependence function; generator of a dependence function; archimax copula; copula; dependence function; generator of a dependence function},
language = {eng},
number = {5},
pages = {977-987},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Constructing families of symmetric dependence functions},
url = {http://eudml.org/doc/251414},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Wysocki, Włodzimierz
TI - Constructing families of symmetric dependence functions
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 5
SP - 977
EP - 987
AB - We construct two pairs $(\mathcal {A}^{[1]}_{F}, \mathcal {A}^{[2]}_{F})$ and $(\mathcal {A}^{[1]}_{\psi }, \mathcal {A}^{[2]}_{\psi })$ 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.
LA - eng
KW - archimax copula; copula; dependence function; generator of a dependence function; archimax copula; copula; dependence function; generator of a dependence function
UR - http://eudml.org/doc/251414
ER -