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, smooth2 = NULL, 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 sill , range , smooth and cov.mod are
given. |
sill,range,smooth,smooth2 |
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", "powexp", "bessel" or
"caugen" for the Whittle-Matern, Cauchy, Powered Exponential, Bessel
and Generalized Cauchy models. May be missing if fitted is
given. |
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, four covariance functions are defined: the Whittle-Matern, powered exponential (also known as "stable"), Cauchy and Bessel models. These covariance functions are defined as follows:
where Gamma is the gamma function, K_smooth and J_smooth are both modified Bessel functions 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 ##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 data <- rmaxstab(30, locations, cov.mod = "whitmat", sill = 1, range = 3, smooth = 1) ##Fit a max-stable model fitted <- fitmaxstab(data, locations, "whitmat", std.err.type = "none", sill = 1) covariance(fitted, ylim = c(0, 1)) covariance(sill = 1, range = 3, smooth = 1, 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)