Likelihood for multivariate peaks over threshold models

Likelihood for the various parametric limiting models over region determined by $$\{y \in F: \max_{j=1}^D \sigma_j \frac{y^\xi_j-1}{\xi_j}+\mu_j > u\};$$ where $\mu$ is loc, $\sigma$ is scale and $\xi$ is shape.

Usage

likmgp(
  dat,
  thresh,
  loc,
  scale,
  shape,
  par,
  model = c("log", "br", "xstud"),
  likt = c("mgp", "pois", "binom"),
  lambdau = 1,
  ...
)

Arguments

dat: matrix of observations
thresh: functional threshold for the maximum
loc: vector of location parameter for the marginal generalized Pareto distribution
scale: vector of scale parameter for the marginal generalized Pareto distribution
shape: vector of shape parameter for the marginal generalized Pareto distribution
par: list of parameters: alpha for the logistic model, Lambda for the Brown--Resnick model or else Sigma and df for the extremal Student.
model: string indicating the model family, one of "log", "neglog", "br" or "xstud"
likt: string indicating the type of likelihood, with an additional contribution for the non-exceeding components: one of "mgp", "binom" and "pois".
lambdau: vector of marginal rate of marginal threshold exceedance.
...: additional arguments (see Details)

Value

the value of the log-likelihood with attributes

expme, giving the exponent measure

Details

Optional arguments can be passed to the function via ...

cl cluster instance created by makeCluster (default to NULL)
ncors number of cores for parallel computing of the likelihood
mmax maximum per column
B1 number of replicates for quasi Monte Carlo integral for the exponent measure
genvec1 generating vector for the quasi Monte Carlo routine (exponent measure), associated with B1

Note

The location and scale parameters are not identifiable unless one of them is fixed.