fmadogram {SpatialExtremes} | R Documentation |
Computes the F-madogram for max-stable processes.
fmadogram(data, coord, n.bins, which = c("mado", "ext"), xlab, ylab, angles = NULL, marge = "mle", ...)
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. |
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 ylab must have the same length has which . |
angles |
A numeric vector. A partition of the interval (-π, π) to help detecting anisotropy. |
marge |
Character string. If 'emp', the probabilities of non exceedances are estimated using the empirical CDF. If 'mle' (default), maximum likelihood estimates are used. |
... |
Additional options to be passed to the plot
function. |
Let Z(x) be a stationary process. The F-madogram is defined as follows:
nu(h) = 0.5 * E[|F(Z(x+h)) - F(Z(x))|]
The extremal coefficient theta(h) satisfies:
(1 + 2 nu(h)) / (1 - 2 nu(h)
A graphic and (invisibly) a matrix with the lag distances, the F-madogram and extremal coefficient estimates.
Mathieu Ribatet
Cooley, D., Naveau, P. and Poncet, P. (2006) Variograms for spatial max-stable random fields. Dependence in Probability and Statistics, 373–390.
require(RandomFields) n.site <- 50 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(0,1,0,1, 2), maxstable="extr", n = 40) ms0 <- t(ms0) ##Compute the F-madogram fmadogram(ms0, locations)