maxstabtest: P-P plot for testing max stability

View source: R/maxstabtest.R

maxstabtestR Documentation

P-P plot for testing max stability


The diagnostic, proposed by Gabda, Towe, Wadsworth and Tawn, relies on the fact that, for max-stable vectors on the unit Gumbel scale, the distribution of the maxima is Gumbel distribution with a location parameter equal to the exponent measure. One can thus consider tuples of size m and estimate the location parameter via maximum likelihood and transforming observations to the standard Gumbel scale. Replicates are then pooled and empirical quantiles are defined. The number of combinations of m vectors can be prohibitively large, hence only nmax randomly selected tuples are selected from all possible combinations. The confidence intervals are obtained by a nonparametric bootstrap, by resampling observations with replacement observations for the selected tuples and re-estimating the location parameter. The procedure can be computationally intensive as a result.


  m = prod(dim(dat)[-1]),
  nmax = 500L,
  B = 1000L,
  ties.method = "random",
  plot = TRUE



matrix or array of max-stable observations, typically block maxima. The first dimension should consist of replicates


integer indicating how many tuples should be aggregated.


maximum number of pairs. Default to 500L.


number of nonparametric bootstrap replications. Default to 1000L.


string indicating the method for rank. Default to "random".


logical indicating whether a graph should be produced (default to TRUE).


a Tukey probability-probability plot with 95


Gabda, D.; Towe, R. Wadsworth, J. and J. Tawn, Discussion of “Statistical Modeling of Spatial Extremes” by A. C. Davison, S. A. Padoan and M. Ribatet. Statist. Sci. 27 (2012), no. 2, 189–192.


## Not run: 
dat <- mev::rmev(n = 250, d = 100, param = 0.5, model = "log")
maxstabtest(dat, m = 100)
maxstabtest(dat, m = 2, nmax = 100)
dat <- mev::mvrnorm(n = 250, Sigma = diag(0.5, 10) + matrix(0.5, 10, 10), mu = rep(0, 10))
maxstabtest(dat, m = 2, nmax = 100)
maxstabtest(dat, m = ncol(dat))

## End(Not run)

mev documentation built on April 20, 2023, 5:10 p.m.