| 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)