par and par2:
| Copula family | par |
par2 |
Gaussian |
| $(-1,1)$ | - |
| Student t | $(-1,1)$ |
| $(2,\infty)$ | (Survival) Clayton |
| $(0,\infty)$ | - |
| (Survival) Gumbel | $[1,\infty)$ |
| - | Frank |
| $R\backslash\{0\}$ | - |
| (Survival) Joe | $(1,\infty)$ |
| - | Rotated Clayton (90 and 270 degrees) |
| $(-\infty,0)$ | - |
| Rotated Gumbel (90 and 270 degrees) | $(-\infty,-1]$ |
| - | Rotated Joe (90 and 270 degrees) |
| $(-\infty,-1)$ | - |
| (Survival) Clayton-Gumbel (BB1) | $(0,\infty)$ |
| $[1,\infty)$ | (Survival) Joe-Gumbel (BB6) |
| $[1,\infty)$ | $[1,\infty)$ |
| (Survival) Joe-Clayton (BB7) | $[1,\infty)$ |
| $(0,\infty)$ | (Survival) Joe-Frank (BB8) |
| $[1,\infty)$ | $(0,1]$ |
| Rotated Clayton-Gumbel (90 and 270 degrees) | $(-\infty,0)$ |
| $-\infty,-1]$ | Rotated Joe-Gumbel (90 and 270 degrees) |
| $(-\infty,-1]$ | $(-\infty,-1]$ |
| Rotated Joe-Clayton (90 and 270 degrees) | $(-\infty,-1]$ |
| $(-\infty,0)$ | Rotated Joe-Frank (90 and 270 degrees) |
| $(-\infty,-1]$ | $[-1,0)$ |
family) and parameters (par and par2) have to be specified as vectors of length $d(d-1)/2$,
where $d$ is the number of variables.
In a C-vine, the entries of this vector correspond to the following pairs and associated pair-copula terms
$(1,2), (1,3), (1,4), ..., (1,d),$
$(2,3|1), (2,4|1), ..., (2,d|1),$
$(3,4|1,2), (3,5|1,2), ..., (3,d|1,2),$
$...,$
$(d-1,d|1,...,d-2).$
Similarly, the pairs of a D-vine are denoted in the following order:
$(1,2), (2,3), (3,4), ..., (d-1,d),$
$(1,3|2), (2,4|3), ..., (d-2,d|d-1),$
$(1,4|2,3), (2,5|3,4), ..., (d-3,d|d-2,d-1),$
$...,$
$(1,d|2,...,d-1).$| Package: |
| CDVine |
| Type: |
| Package |
| Version: |
| 1.4 |
| Date: |
| 2015-10-29 |
| License: |
| GPL (>=2) |
| Depends: |
| R ($>= 2.11.0$) |
| Imports: MASS, mvtnorm, graphics, igraph, stats |
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Bedford, T. and R. M. Cooke (2002). Vines - a new graphical model for dependent random variables. Annals of Statistics 30, 1031-1068.
Brechmann, E. C., C. Czado, and K. Aas (2012). Truncated regular vines in high dimensions with applications to financial data. Canadian Journal of Statistics 40 (1), 68-85.
Brechmann, E. C. and C. Czado (2011). Risk Management with High-Dimensional Vine Copulas: An Analysis of the Euro Stoxx 50. Submitted for publication. http://mediatum.ub.tum.de/doc/1079276/1079276.pdf.
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Joe, H. (1996). Families of m-variate distributions with given margins and m(m-1)/2 bivariate dependence parameters. In L. Rueschendorf, B. Schweizer, and M. D. Taylor (Eds.), Distributions with fixed marginals and related topics, pp. 120-141. Hayward: Institute of Mathematical Statistics.
Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman and Hall, London.
Knight, W. R. (1966). A computer method for calculating Kendall's tau with ungrouped data. Journal of the American Statistical Association 61 (314), 436-439.
Kurowicka, D. and R. M. Cooke (2006). Uncertainty Analysis with High Dimensional Dependence Modelling. Chichester: John Wiley.
Kurowicka, D. and H. Joe (Eds.) (2011). DEPENDENCE MODELING: Vine Copula Handbook. Singapore: World Scientific Publishing Co.