fmadogram: Computes the F-madogram

In SpatialExtremes: Modelling Spatial Extremes

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 fitmaxstab function. May be missing.
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.
col	The colors used for the points and optionnaly the fitted curve.
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.
add	Logical. If TRUE, the plot is added to the current figure; otherwhise (default) a new plot is computed.
xlim	A numeric vector of length 2 specifying the x coordinate range.
...	Additional options to be passed to the plot function.

Details

Let Z(x) be a stationary process. The F-madogram is defined as follows:

ν(h) = 0.5 * E[|F(Z(x+h)) - F(Z(x))|]

The extremal coefficient θ(h) satisfies:

{1 + 2 ν(h)} / {1 - 2 ν(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

madogram, lmadogram

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")

SpatialExtremes documentation built on April 19, 2022, 5:06 p.m.