qqgev: QQ-plot for the GEV parameters

Description

This function compares the GEV parameters estimated separately for each location to the ones estimated from a fitted spatial model.

Usage

qqgev(fitted, xlab, ylab, ...)

Arguments

fitted

An object of class maxstab or spatgev. Most often, this will be the output of fitmaxstab, fitcovmat,

xlab,ylab

The x and y-axis labels. May be missing.

...

Optional arguments to be passed to the plot function.

Value

A QQ-plot.

References

Schlather, M. (2002) Models for Stationary Max-Stable Random Fields. Extremes 5:1, 33--44. Schlather, M. and Tawn, J. A. (2003) A dependence measure for multivariate and spatial extreme values: Properties and inference. Biometrika 90(1):139--156.

Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.

Examples

Run this code

require(RandomFields)

##Define the coordinate of each location
n.site <- 30
locations <- matrix(runif(2*n.site, 0, 10), ncol = 2)
colnames(locations) <- c("lon", "lat")

##Simulate a max-stable process - with unit Frechet margins
sigma <- matrix(c(100, 25, 25, 220),ncol = 2)
sigma.inv <- solve(sigma)
sqrtCinv <- t(chol(sigma.inv))
model <- list(list(model = "gauss", var = 1, aniso = sqrtCinv / 2))
ms0 <- MaxStableRF(locations[,1], locations[,2], grid=FALSE, model=model,
                   maxstable="Bool", n = 40)
ms0 <- t(ms0)

##Now define the spatial model for the GEV parameters
param.loc <- -10 + 2 * locations[,2]
param.scale <- 5 + 2 * locations[,1] + locations[,2]^2
param.shape <- rep(0.2, n.site)

##Transform the unit Frechet margins to GEV 
for (i in 1:n.site)
  ms0[,i] <- frech2gev(ms0[,i], param.loc[i], param.scale[i], param.shape[i])

##Define a model for the GEV margins to be fitted
##shape ~ 1 stands for the GEV shape parameter is constant
##over the region
loc.form <- loc ~ lat
scale.form <- scale ~ lon + I(lat^2)
shape.form <- shape ~ 1

fitted <- fitspatgev(ms0, locations, loc.form = loc.form, scale.form =
scale.form, shape.form = shape.form)

qqgev(fitted)