amvnonpar {evd}R Documentation

Non-parametric Estimates for Dependence Functions of the Trivariate Extreme Value Distribution

Description

Calculate or plot non-parametric estimates for the dependence function A of the trivariate extreme value distribution.

Usage

amvnonpar(x = rep(1/3,3), data, epmar = FALSE, nsloc1 = NULL, nsloc2 =
    NULL, nsloc3 = NULL, madj = 0, 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)

Arguments

x A vector of length three or a matrix with three 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(1/3,1/3,1/3) is returned by default since it is often a useful summary of dependence.
data A matrix or data frame with three columns, which may contain missing values.
epmar If TRUE, an empirical transformation of the marginals is performed in preference to marginal parametric GEV estimation, and the nsloc arguments are ignored.
nsloc1, nsloc2, nsloc3 A data frame with the same number of rows as data, for linear modelling of the location parameter on the first/second/third margin. The data frames are treated as covariate matrices, excluding the intercept. A numeric vector can be given as an alternative to a single column data frame.
madj Performs marginal adjustments. See abvnonpar.
plot Logical; if TRUE the function is plotted. The minimum (evaluated) value is returned invisibly. If FALSE (the default), the following arguments are ignored.
col 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.
blty 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.
grid For plotting, the function is evaluated at grid^2 points.
lower The minimum value for which colours are plotted. By default lower = 1/3 as this is the theoretical minimum of the dependence function of the trivariate extreme value distribution.
ord 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.
lab A character vector of length three, in which case the ith margin is labelled using the ith 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.
lcex A numerical value giving the amount by which the labels should be scaled relative to the default. Ignored if lab is NULL.

Value

amvnonpar calculates or plots a non-parametric estimate of the dependence function of the trivariate extreme value distribution.

Note

The rows of data that contain missing values are not used in the estimation of the dependence structure, but every non-missing value is used in estimating the margins.

The dependence function of the trivariate extreme value distribution is defined in amvevd. The function amvevd calculates and plots dependence functions of trivariate logistic and trivariate asymmetric logistic models.

The estimator plotted or calculated is a trivariate extension of the bivariate Pickands estimator defined in abvnonpar.

See Also

amvevd, abvnonpar, fgev

Examples

s3pts <- matrix(rexp(30), nrow = 10, ncol = 3)
s3pts <- s3pts/rowSums(s3pts)
sdat <- rmvevd(100, dep = 0.6, model = "log", d = 3)
amvnonpar(s3pts, sdat)

## Not run: amvnonpar(data = sdat, plot = TRUE)
## Not run: amvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
## Not run: amvevd(dep = 0.6, model = "log", plot = TRUE)
## Not run: amvevd(dep = 0.6, model = "log", plot = TRUE, blty = 1)

[Package evd version 2.2-0 Index]