fitextcoeff {SpatialExtremes} | R Documentation |
Estimates non parametrically the extremal coefficient function.
fitextcoeff(data, coord, ..., estim = "ST", marge = "emp", prob = 0, plot = TRUE, loess = TRUE, method = "BFGS", std.err = TRUE, xlab, ylab, angles = NULL, identify = FALSE)
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. |
... |
Additional options to be passed to the plot
function. |
estim |
Character string specifying the estimator to be used. Must be one of "ST" (Schlather and Tawn) or "Smith". |
marge |
Character string specifying how margins are transformed to unit Frechet. Must be one of "emp", "mle" or "none" - see Details |
prob |
The probability related to the threshold. Only useful with
the ST estimator. |
plot |
Logical. If TRUE (default), the extremal
coefficient function is plotted |
loess |
If TRUE (default), a local polynomial curve is
plotted - see function loess . |
method |
The optimizer used when fitting the GEV distribution to
data. See function gevmle . |
std.err |
Logical. If TRUE , standard errors are
computed. Note that standard errors are not available with the "ST"
estimator. |
xlab,ylab |
The x-axis and y-axis labels. May be missing. |
angles |
A numeric vector. A partition of the interval (-π, π) to help detecting anisotropy. |
identify |
Logical. If TRUE , users can use the
identify function to identify pairs of stations on the
plot. |
During the estimation procedure, data need to be transformed to unit Frechet margins firts. This can be done in two different ways ; by using the empirical CDF or the GEV ML estimates.
If marge = "emp"
, then the data are transformed using the
following relation:
z_i = - 1 / log(F(y_i))
where y_i are the observations available at location i, F is the empirical CDF and z_i are the observations transformed to unit Frechet scale.
If marge = "mle"
, then the data are transformed using the MLE
of the GEV distribution - see function gev2frech
.
Lastly, if data are already supposed to be unit Frechet, then no
transformation is performed if one passed the option marge =
"frech"
.
If data
are already componentwise maxima, prob
should be
zero. Otherwise, users have to define a threshold z (large
enough) where univariate extreme value arguments are relevant. We
define prob
such that Pr[Z <= z] =
prob.
Plots the extremal coefficient function and returns the points used
for the plot. If loess = TRUE
, the output is a list with
argument "ext.coeff" and "loess".
Mathieu Ribatet
Schlather, M. and Tawn, J. A. (2003) A dependence measure for multivariate and spatial extreme values: Properties and inference. Biometrika 90(1):139–156.
Smith, R. L. (1990) Max-stable processes and spatial extremes. Unpublished manuscript.
require(RandomFields) n.site <- 30 locations <- matrix(runif(2*n.site, 0, 10), ncol = 2) colnames(locations) <- c("lon", "lat") ##Simulate a max-stable process - with unit Frechet margins sigma <- matrix(c(10, 40, 40, 220),ncol = 2) sigma.inv <- solve(sigma) sqrtCinv <- t(chol(sigma.inv)) model <- list(list(model = "gauss", var = 1, aniso = sqrtCinv / 2)) ms0 <- MaxStableRF(locations[,1], locations[,2], grid=FALSE, model=model, maxstable="Bool", n = 40) ms0 <- t(ms0) ##Plot the extremal coefficient function op <- par(mfrow=c(1,2)) fitextcoeff(ms0, locations, estim = "Smith") fitextcoeff(ms0, locations, angles = seq(-pi, pi, length = 4), estim = "Smith") par(op)