Calculate non-parametric estimates for the dependence function \(A\) of the multivariate extreme value distribution and plot the estimated function in the trivariate case.
amvnonpar(x = rep(1/d,d), data, d = 3, epmar = FALSE, nsloc = NULL,
madj = 0, kmar = NULL, plot = FALSE, col = heat.colors(12),
blty = 0, grid = if(blty) 150 else 50, lower = 1/3, ord = 1:3,
lab = as.character(1:3), lcex = 1)
A numeric vector of estimates. If plotting, the smallest evaluated estimate is returned invisibly.
A vector of length d
or a matrix with d
columns, in which case the dependence function is evaluated
across the rows (ignored if plot is TRUE
). The
elements/rows of the vector/matrix should be positive and should
sum to one, or else they should have a positive sum, in which
case the rows are rescaled and a warning is given.
\(A(1/d,\dots,1/d)\) is returned by default since it is often
a useful summary of dependence.
A matrix or data frame with d
columns, which may
contain missing values.
The dimension; an integer greater than or equal to two.
The trivariate case d = 3
is the default.
If TRUE
, an empirical transformation of the
marginals is performed in preference to marginal parametric
GEV estimation, and the nsloc
argument is ignored.
A data frame with the same number of rows as data
,
or a list containing d
elements of this type, for linear
modelling of the marginal location parameters. In the former case,
the argument is applied to all margins. The data frames are treated
as covariate matrices, excluding the intercept. Numeric vectors can
be given as alternatives to single column data frames. A list can
contain NULL
elements for stationary modelling of selected
margins.
Performs marginal adjustments. See
abvnonpar
.
In the rare case that the marginal distributions are known, specifies the GEV parameters to be used instead of maximum likelihood estimates.
Logical; if TRUE
, and the dimension d
is
three (the default dimension), the dependence function of a
trivariate extreme value distribution is plotted. For plotting in
the bivariate case, use abvnonpar
. If FALSE
(the default), the following arguments are ignored.
A list of colours (see image
). The first
colours in the list represent smaller values, and hence
stronger dependence. Each colour represents an equally spaced
interval between lower
and one.
The border line type, for the border that surrounds
the triangular image. By default blty
is zero, so no
border is plotted. Plotting a border leads to (by default) an
increase in grid
(and hence computation time), to ensure
that the image fits within it.
For plotting, the function is evaluated at grid^2
points.
The minimum value for which colours are plotted. By default \(\code{lower} = 1/3\) as this is the theoretical minimum of the dependence function of the trivariate extreme value distribution.
A vector of length three, which should be a permutation
of the set \(\{1,2,3\}\). The points \((1,0,0)\),
\((0,1,0)\) and \((0,0,1)\) (the vertices of the simplex)
are depicted clockwise from the top in the order defined by
ord
. The argument alters the way in which the function
is plotted; it does not change the function definition.
A character vector of length three, in which case the
i
th margin is labelled using the i
th component,
or NULL
, in which case no labels are given. By default,
lab
is as.character(1:3)
. The actual location of
the margins, and hence the labels, is defined by ord
.
A numerical value giving the amount by which the
labels should be scaled relative to the default. Ignored
if lab
is NULL
.
amvevd
, abvnonpar
,
fgev
s5pts <- matrix(rexp(50), nrow = 10, ncol = 5)
s5pts <- s5pts/rowSums(s5pts)
sdat <- rmvevd(100, dep = 0.6, model = "log", d = 5)
amvnonpar(s5pts, sdat, d = 5)
if (FALSE) amvnonpar(data = sdat, plot = TRUE)
if (FALSE) amvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
if (FALSE) amvevd(dep = 0.6, model = "log", plot = TRUE)
if (FALSE) amvevd(dep = 0.6, model = "log", plot = TRUE, blty = 1)
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