mev (version 1.3)

rmevspec: Random samples from spectral distributions of multivariate extreme value models.

Description

Generate from $Q_i$, the spectral measure of a given multivariate extreme value model

Usage

rmevspec(n, d, param, sigma, model = c("log", "neglog", "bilog", "negbilog",
  "hr", "xstud", "ct", "dirmix"), weights, vario, loc)

Arguments

n

number of observations

d

dimension of sample

param

parameter vector for the logistic, bilogistic, negative bilogistic and Dirichlet (Coles and Tawn) model. Parameter matrix for the Dirichlet mixture. Degree of freedoms for extremal student model.

sigma

covariance matrix for Husler-Reiss and extremal Student-t distributions

model

choice between 1-parameter logistic and negative logistic, bilogistic, negative bilogistic and extremal Dirichlet, the Brown-Resnick and extremal Student max-stable process (which generate the Husler-Reiss MEV distribution), or the Dirichlet mixture.

weights

vector of length m for the m mixture components. Must sum to one

vario

function specifying the variogram. Used only if provided in conjonction with loc and if sigma is missing

loc

d by k matrix of location, used as input in the variogram vario or as parameter in the Smith smith model.

Value

• an n by d exact sample from the corresponding multivariate extreme value model

Details

The vector param differs depending on the model

• log: one dimensional parameter greater than 1
• neglog: one dimensional positive parameter
• bilog:d-dimensional vector of parameters in$[0,1]$
• negbilog:d-dimensional vector of negative parameters
• ct:d-dimensional vector of positive (a)symmetry parameters. Alternatively, a$d+1$vector consisting of thedDirichlet parameters and the last entry is an index of regular variation in(0, 1]treated as scale
• xstud: one dimensional parameter corresponding to degrees of freedomalpha
• dirmix:dbym-dimensional matrix of positive (a)symmetry parameters

References

Dombry, Engelke and Oesting (2015). Exact simulation of max-stable processes, arXiv:1506.04430v1, 1--24.

Boldi (2009). A note on the representation of parametric models for multivariate extremes. Extremes 12, 211--218.

Examples

set.seed(1)
rmevspec(n=100, d=3, param=2.5, model="log")
rmevspec(n=100, d=3, param=2.5, model="neglog")
rmevspec(n=100, d=4, param=c(0.2,0.1,0.9,0.5), model="bilog")
rmevspec(n=100, d=2, param=c(0.8,1.2), model="ct") #Dirichlet model
rmevspec(n=100, d=2, param=c(0.8,1.2,0.5), model="ct") #with additional scale parameter
#Variogram gamma(h) = scale*||h||^alpha
scale <- 0.5; alpha <- 1
vario <- function(x) scale*sqrt(sum(x^2))^alpha
#grid specification
grid.loc <- as.matrix(expand.grid(runif(4), runif(4)))
rmevspec(n=100, vario=vario,loc=grid.loc, model="hr")
## Example with Dirichlet mixture
alpha.mat <- cbind(c(2,1,1),c(1,2,1),c(1,1,2))
rmevspec(n=100, param=alpha.mat, weights=rep(1/3,3), model="dirmix")