Constructing families of symmetric dependence functions
Kybernetika (2012)
- Volume: 48, Issue: 5, page 977-987
- ISSN: 0023-5954
Access Full Article
topAbstract
topHow to cite
topWysocki, 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 -
References
top- Capéraà, P., Fougères, A. L., Genest, C., 10.1006/jmva.1999.1845, J. Multivariate Anal. 72 (2000), 30-49. Zbl0978.62043MR1747422DOI10.1006/jmva.1999.1845
- Genest, C., MacKay, J., 10.2307/3314660, Canad. J. Statist. 14 (1986), 145-159. MR0849869DOI10.2307/3314660
- Gudendorf, G., Segers, J., Extreme-value copulas., In: Copula Theory and Its Applications, Warsaw 2009, Lecture Notes in Statist. Proc. 198, Springer 2010, pp. 127-146.
- Gumbel, E. J., 10.1080/01621459.1960.10483368, J. Amer. Statist. Assoc. 55 (1960), 698-707. Zbl0099.14501MR0116403DOI10.1080/01621459.1960.10483368
- Hürlimann, W., Properties and measures of dependence for the archimax copula., Adv. Appl. Statist. 5 (2005), 125-143. MR2204874
- Hutchinson, T. P., Lai, C. D., Continuous Bivariate Distributions. Emphasising Applications., Rumsby Sci. Publ., Adelaide 1990. Zbl1170.62330MR1070715
- Joe, H., Multivariate Models and Dependence Concepts., Chapman and Hall, London 1997. Zbl0990.62517MR1462613
- Nelsen, R. B., An Introduction to Copulas., Springer, New York 1999. Zbl1152.62030MR1653203
- Pickands, J., Multivariate extreme value distributions., Bull. Int. Statist. Inst. 49 (1981), 859-879. Zbl0518.62045MR0820979
- Wysocki, W., When a copula is archimax., Statist. Probab. Lett. (2012), to appear.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.