SpatialExtremes (version 1.1-1)

lmadogram: Computes the lambda-madogram

Description

Computes the lambda-madogram for max-stable processes.

Usage

lmadogram(data, coord, n.bins, xlab, ylab, zlab, n.lambda = 11, marge =
"mle", 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.

Value

• A graphic and (invisibly) a matrix with the lag distances, the $\lambda$-madogram estimate.

Details

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

$$\nu_{\lambda}(h) = \frac{1}{2}\mbox{E}\left[|F^\lambda(Z(x+h)) - F^{1-\lambda}(Z(x))| \right]$$

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
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 lambda-madogram
lmadogram(ms0, locations, n.bins = 80)