A User’s Guide to the SpatialExtremes Package

1.1 Two simulations of the Smith model with different Σ matrices. Left panel: σ 11 = σ 22 = 9/8 and σ 12 = 0. Right panel: σ 11 = σ 22 = 9/8 and σ 12 = 1. The max-stable processes are transformed to unit Gumbel margins for viewing purposes.. 6 1.2 Plots of the Whittle–Matérn, the powered exponential, the Cauchy and the Bessel correlation functions-from left to right. The sill and the range parameters are c 1 = c 2 = 1 while the smooth parameters are given in the legends.. .. .. .. . 7 1.3 Two simulations of the Schlather model with different correlation functions having approximately the same practical range. Left panel: Whittle–Matérn with c 1 = c 2 = ν = 1. Right panel: Powered exponential with c 1 = ν = 1 and c 2 = 1.5. The max-stable processes are transformed to unit Gumbel margins for viewing 1.4 Contour plots of an isotropic (left panel) and anisotropic (right panel) correlation function. Powered exponential family with c 1 = c 2 = ν = 1. The anisotropy parameters are: ϕ = π/4, r = 0. 2.1 One realisation of a gaussian random field having a Whittle-Matern covariance function with sill, range and smooth parameters all equal to one using the turning bands methods. The continuous spectral method was used for simulating processes on the lines. The observations are transformed to unit Gumbel margins for viewing purposes.. .. 16 3.1 Extremal coefficient functions for different max-stable models. Σ is the 2 × 2 identity matrix. Correlation function: Whittle–Matérn with c 1 = c 2 = ν = 1.. . 20 3.2 Pairwise extremal coefficient estimates from the Schlather and Tawn (left panel) and Smith (right panel) estimators from a simulated max-stable random field having a Whittle–Matérn correlation function-c 1 = c 2 = ν = 1. The red lines are the theoretical extremal coefficient function.. 3.3 Madogram (left panel) and binned madogram (right panel) with unit Gumbel margins for the Schlather model with the Whittle–Matérn correlation functions. The red lines are the theoretical madograms. Points are pairwise estimates.. .. 23 3.4 Pairwise madograms (left panel) and extremal coefficients (right panel) estimates from a simulated max-stable random field having a Whittle–Matérn correlation function-c 1 = c 2 = ν = 1. The red lines are the theoretical madogram and extremal coefficient function. .