R: Computes the F-madogram

fmadogram {SpatialExtremes} | R Documentation

## 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")

[Package SpatialExtremes version 2.0-5 Index]