| covariance {SpatialExtremes} | R Documentation |
This function defines and computes several covariance function either from a fitted ``max-stable'' model; either by specifying directly the covariance parameters.
covariance(fitted, sill, range, smooth, cov.mod = "whitmat", plot = TRUE, dist, xlab, ylab, ...)
fitted |
An object of class ``maxstab''. Most often this will be
the output of the fitmaxstab function. May be missing
if scale and smooth are given. |
sill,range,smooth |
The sill, scale and smooth parameters for
the covariance function. May be missing if fitted is given. |
cov.mod |
Character string. The name of the covariance model. Must be one of "whitmat", "cauchy" or "powexp" for the Whittle-Matern, Cauchy and Powered Exponential models. |
plot |
Logical. If TRUE (default) the covariance function
is plotted. |
dist |
A numeric vector corresponding to the distance at which the covariance function should be evaluated. May be missing. |
xlab,ylab |
The x-axis and y-axis labels. May be missing. |
... |
Several option to be passed to the plot
function. |
This function returns the covariance function. Eventually, if
dist is given, the covariance function is computed for each
distance given by dist. If plot = TRUE, the covariance
function is plotted.
Mathieu Ribatet
## 1- Calling covariance using fixed covariance parameters
covariance(sill = 1, range = 1, smooth = 0.5, cov.mod = "whitmat")
covariance(sill = 0.5, range = 1, smooth = 0.5, cov.mod = "whitmat",
dist = seq(0,5, 0.2), plot = FALSE)
## 2- Calling covariance from a fitted model
## Not run:
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
ms0 <- MaxStableRF(locations[,1], locations[,2], grid=FALSE, model="wh",
param=c(0,1,0,3, .5), maxstable="extr",
n = 30)
ms1 <- 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)
ms1[,i] <- param.scale[i] * (ms1[,i]^param.shape[i] - 1) /
param.shape[i] + param.loc[i]
##Define a model for the GEV margins to be fitted
##shape ~ 1 stands for a constant GEV shape parameter
##over the region
loc.form <- loc ~ lat
scale.form <- scale ~ lon + I(lat^2)
shape.form <- shape ~ 1
fitted <- fitmaxstab(ms1, locations, "whitmat", loc.form, scale.form,
shape.form)
covariance(fitted, ylim = c(0, 1))
covariance(sill = 1, range = 3, smooth = .5, cov.mod = "whitmat", add = TRUE, col
= 3)
title("Whittle-Matern covariance function")
legend("topright", c("Theo.", "Fitted"), lty = 1, col = c(3,1), inset =
.05)
## End(Not run)