Description Usage Arguments Details Value Author(s) References See Also Examples
Computes the madogram for max-stable processes.
1 2 3 |
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
|
n.bins |
The number of bins to be used. If missing, pairwise madogram estimates will be computed. |
gev.param |
Numeric vector of length 3 specifying the location, scale and shape parameters for the GEV. |
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 |
col |
The colors used for the points and optionnaly for the fitted curve. |
angles |
A numeric vector. A partition of the interval (0, π) to help detecting anisotropy. |
marge |
Character string. If 'emp', the observation are first transformed to the unit Frechet scale by using the empirical CDF. If 'mle' (default), maximum likelihood estimates are used. |
add |
Logical. If |
xlim |
A numeric vector of length 2 specifying the x coordinate range. |
... |
Additional options to be passed to the |
Let Z(x) be a stationary process. The madogram is defined as follows:
ν(h) = 0.5 * E[|Z(x+h) - Z(x)|]
If now Z(x) is a stationary max-stable random field with GEV marginals. Provided the GEV shape parameter ξ is such that ξ <1. The extremal coefficient θ(h) satisfies:
u_β (μ + ν(h) / Γ(1 - ξ)), if ξ < 1, exp(ν(h)/σ), otherwise
where Γ is the gamma function and u_β is defined as follows:
(1 + ξ (u - μ) / σ )_+^{1/ξ}
and β= (μ, σ, ξ), i.e, the vector of the GEV parameters.
A graphic and (invisibly) a matrix with the lag distances, the 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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | 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 madogram
madogram(data, locations)
##Compare the madogram with a fitted max-stable model
fitted <- fitmaxstab(data, locations, "whitmat", nugget = 0)
madogram(fitted = fitted, which = "ext")
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