fmadogram: Computes the F-madogram
In SpatialExtremes: Modelling Spatial Extremes

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the F-madogram for max-stable processes.

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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)), ...)

`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.

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)}

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.

madogram, lmadogram

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")