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 sill , range , smooth and cov.mod 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", "powexp" or "bessel" for
the Whittle-Matern, Cauchy, Powered Exponential and Bessel
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 Γ is the gamma function, K_smooth is the modified Bessel function of order smooth and J_smooth is the 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 ##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 = 0.5) ##Fit a max-stable model fitted <- fitmaxstab(data, locations, "whitmat", std.err.type = "none") 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)