ec {satdad} | R Documentation |
Extremal coefficients for Mevlog models.
Description
Theoretical extremal coefficients for Mevlog models. A Mevlog
model is a multivariate extreme value (symmetric or asymmetric) logistic model.
Usage
ec(ds, ind = 2, norm = FALSE)
Arguments
ds |
An object of class |
ind |
A character string among "with.singletons" and "all" (without singletons), or an integer in |
norm |
A boolean. 'FALSE' (the default): ec is computed. 'TRUE': inverse normalized ec is computed. |
Details
The tail dependence structure is set by a ds
object. It thus corresponds to the stable tail dependence function . The way to deduce the stable tail dependence function
from
ds
is explained in the Details section of gen.ds
.
Value
The function returns a list of two elements:
subsets
A list of subsets from.
When
ind
is given as an integer,subsets
is the list of subsets fromwith cardinality
ind
. Whenind
is the list, it corresponds tosubsets
.When
ind = "with.singletons"
subsets is the list of all non empty subsets in.
When
ind = "all"
subsets is the list of all subsets inwith cardinality larger or equal to 2.
ec
A vector of theoretical extremal coefficients associated with the listsubsets
.An extremal coefficient associated with the subset
is
. Its value lies in
.
When
norm = TRUE
, then inverse normalized ec are computed by.
Author(s)
Cécile Mercadier (mercadier@math.univ-lyon1.fr
)
References
Mercadier, C. and Roustant, O. (2019) The tail dependograph. Extremes, 22, 343–372.
Tiago de Oliveira, J. (1962/63) Structure theory of bivariate extremes, extensions. Estudos de Matematica, Estatistica, e Economicos, 7:165–195.
Smith, R. L. (1990) Max-stable processes and spatial extremes. Dept. of Math., Univ. of Surrey, Guildford GU2 5XH, England.
See Also
ellMevlog
, gen.ds
, graphs
, tsic
Examples
## Fix a 4-dimensional asymmetric tail dependence structure
ds4 <- gen.ds(d = 4)
## Compute all theoretical extremal coefficients
ec(ds = ds4, ind = "with.singletons")
## Compute theoretical extremal coefficients associated with the support of ds4
ec(ds = ds4, ind = ds4$sub)
## Fix a 6-dimensional asymmetric tail dependence structure
ds6 <- gen.ds(d = 6, sub = list(1:2,2:5,5:6))
## Compute all theoretical extremal coefficients on subsets with cardinality 5
ec(ds = ds6, ind = 5)
## Compute inverse renormalized ec
ec(ds = ds6, ind = list(1:2,1:4,1:6), norm = TRUE)