| Title:
|
Constructing families of symmetric dependence functions (English) |
| Author:
|
Wysocki, Włodzimierz |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
5 |
| Year:
|
2012 |
| Pages:
|
977-987 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
archimax copula |
| Keyword:
|
copula |
| Keyword:
|
dependence function |
| Keyword:
|
generator of a dependence function |
| MSC:
|
62H20 |
| idMR:
|
MR3086864 |
| . |
| Date available:
|
2012-12-17T13:39:06Z |
| Last updated:
|
2013-09-24 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143094 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[10] Wysocki, W.: When a copula is archimax..Statist. Probab. Lett. (2012), to appear. |
| . |
