lmadogram: Computes the lambda-madogram

In SpatialExtremes: Modelling Spatial Extremes

Description

Computes the lambda-madogram for max-stable processes.

Usage

lmadogram(data, coord, n.bins, xlab, ylab, zlab, n.lambda = 11, marge =
"emp", col = terrain.colors(50, alpha = 0.5), theta = 90, phi = 20,
border = NA, ...)

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.
n.bins	The number of bins to be used. If missing, pairwise lambda-madogram estimates will be computed.
xlab,ylab,zlab	The x-axis, y-axis and z-axis labels. May be missing.
n.lambda	Integer giving the number of lambda values.
marge	Character string. If 'emp', probabilities of non exceedances are estimated using the empirical CDF. If 'mle' (default), maximum likelihood estimates are used.
col	The colors used to emphasize the gradient of the lambda-madogram.
theta,phi,border	Options to be passed to the persp function.
...	Additional options to be passed to the persp function.

Details

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

ν_λ(h) = 0.5 * E[|F^λ(Z(x+h)) - F^(1-λ)(Z(x))|]

Value

A graphic and (invisibly) a matrix with the lag distances, the λ-madogram estimate.

Author(s)

Mathieu Ribatet

References

Naveau, P., Guillou, A., Cooley, D. and Diebolt, J. (2009) Modelling Pairwise Dependence of Maxima in Space. To appear in Biometrika.

See Also

madogram, fmadogram

Examples

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
data <- rmaxstab(40, locations, cov.mod = "whitmat", nugget = 0, range = 1,
smooth = 2)

##Compute the lambda-madogram
lmadogram(data, locations, n.bins = 80)

Example output

SpatialExtremes documentation built on Sept. 1, 2020, 3:01 a.m.