Exponent measure for multivariate generalized Pareto distributions
Source:R/mgplikelihoods.R
expme.RdIntegrated intensity over the region defined by \([0, z]^c\) for logistic, Huesler-Reiss, Brown-Resnick and extremal Student processes.
Note
The list par must contain different arguments depending on the model. For the Brown–Resnick model, the user must supply the conditionally negative definite matrix Lambda following the parametrization in Engelke et al. (2015) or the covariance matrix Sigma, following Wadsworth and Tawn (2014). For the Husler–Reiss model, the user provides the mean and covariance matrix, m and Sigma. For the extremal student, the covariance matrix Sigma and the degrees of freedom df. For the logistic model, the strictly positive dependence parameter alpha.
Examples
if (FALSE) { # \dontrun{
# Extremal Student
Sigma <- stats::rWishart(n = 1, df = 20, Sigma = diag(10))[, , 1]
expme(z = rep(1, ncol(Sigma)), par = list(Sigma = cov2cor(Sigma), df = 3), model = "xstud")
# Brown-Resnick model
D <- 5L
loc <- cbind(runif(D), runif(D))
di <- as.matrix(dist(rbind(c(0, ncol(loc)), loc)))
semivario <- function(d, alpha = 1.5, lambda = 1) {
(d / lambda)^alpha
}
Vmat <- semivario(di)
Lambda <- Vmat[-1, -1] / 2
expme(z = rep(1, ncol(Lambda)), par = list(Lambda = Lambda), model = "br", method = "mvPot")
Sigma <- outer(Vmat[-1, 1], Vmat[1, -1], "+") - Vmat[-1, -1]
expme(z = rep(1, ncol(Lambda)), par = list(Lambda = Lambda), model = "br", method = "mvPot")
} # }