satdad (version 1.1)

ec: 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)

Value

The function returns a list of two elements:

• subsets A list of subsets from \(\{1,...,d\}\).

  When ind is given as an integer, subsets is the list of subsets from \(\{1,...,d\}\) with cardinality ind. When ind is the list, it corresponds to subsets.

  When ind = "with.singletons" subsets is the list of all non empty subsets in \(\{1,...,d\}\).

  When ind = "all" subsets is the list of all subsets in \(\{1,...,d\}\) with cardinality larger or equal to 2.

• ec A vector of theoretical extremal coefficients associated with the list subsets.

  An extremal coefficient associated with the subset \(I\) is \(\ell(1_I,0_{I^c})\). Its value lies in \((1, |I|)\).

  When norm = TRUE, then inverse normalized ec are computed by \(\dfrac{|I|-ec}{|I|-1}\).

Arguments

ds

An object of class ds.

ind

A character string among "with.singletons" and "all" (without singletons), or an integer in \(\{2,...,d\}\) or a list of subsets from \(\{1,...,d\}\). The default is ind = 2, all pairwise coefficients are computed.

norm

A boolean. `FALSE` (the default): ec is computed. `TRUE`: inverse normalized ec is computed.

Author

Cécile Mercadier ([e-mail])

Details

The tail dependence structure is set by a ds object. It thus corresponds to the stable tail dependence function \(\ell\). The way to deduce the stable tail dependence function \(\ell\) from ds is explained in the Details section of gen.ds.

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)