R: Computes the lambda-madogram

lmadogram {SpatialExtremes} | R Documentation

## 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 =
    "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)

[Package SpatialExtremes version 2.0-5 Index]