fmadogram {SpatialExtremes} | R Documentation |
Computes the F-madogram
Description
Computes the F-madogram for max-stable processes.
Usage
fmadogram(data, coord, fitted, n.bins, which = c("mado", "ext"), xlab,
ylab, col = c(1, 2), angles = NULL, marge = "emp", add = FALSE, xlim =
c(0, max(dist)), ...)
Arguments
data |
A matrix representing the data. Each column corresponds to one location. |
coord |
A matrix that gives the coordinates of each location. Each row corresponds to one location. |
fitted |
An object of class maxstab - usually the output of the
|
n.bins |
The number of bins to be used. If missing, pairwise F-madogram estimates will be computed. |
which |
A character vector of maximum size 2. It specifies if the madogram and/or the extremal coefficient functions have to be plotted. |
xlab , ylab |
The x-axis and y-axis labels. May be missing. Note
that |
col |
The colors used for the points and optionnaly the fitted curve. |
angles |
A numeric vector. A partition of the interval
|
marge |
Character string. If 'emp', the probabilities of non exceedances are estimated using the empirical CDF. If 'mle' (default), maximum likelihood estimates are used. |
add |
Logical. If |
xlim |
A numeric vector of length 2 specifying the x coordinate range. |
... |
Additional options to be passed to the |
Details
Let Z(x)
be a stationary process. The F-madogram is
defined as follows:
\nu(h) = \frac{1}{2}\mbox{E}\left[|F(Z(x+h)) - F(Z(x))|
\right]
The extremal coefficient \theta(h)
satisfies:
\theta(h) = \frac{1 + 2 \nu(h)}{1 - 2 \nu(h)}
Value
A graphic and (invisibly) a matrix with the lag distances, the F-madogram and extremal coefficient estimates.
Author(s)
Mathieu Ribatet
References
Cooley, D., Naveau, P. and Poncet, P. (2006) Variograms for spatial max-stable random fields. Dependence in Probability and Statistics, 373–390.
See Also
Examples
n.site <- 15
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(40, locations, cov.mod = "whitmat", nugget = 0, range = 1,
smooth = 2)
##Compute the F-madogram
fmadogram(data, locations)
##Compare the F-madogram with a fitted max-stable process
fitted <- fitmaxstab(data, locations, "whitmat", nugget = 0)
fmadogram(fitted = fitted, which = "ext")