| 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. |
Currently, three covariance functions are defined: the Whittle-Matern, powered exponential (also known as "stable") and the Cauchy models. These covariance functions are defined as follows:
where Γ is the gamma function and K_smooth is the modified Bessel function of order smooth.
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)