evd (version 2.1-0)

atvnonpar: 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

atvnonpar(x = rep(1/3,3), data, nsloc1 = NULL, nsloc2 = NULL, nsloc3 = NULL,
    method = c("pickands", "deheuvels", "hall"), 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

data

A matrix or data frame with three columns, which may contain missing values.

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 vect

method

The estimation method; a character string. Must be either "pickands" (the default), "deheuvels" or "hall" (or any unique partial match). The three estimators are very similar, and may not be distinguishab

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 a

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

grid

For plotting, the function is evaluated at grid^2 points.

lower

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.

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.

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)

lcex

A numerical value giving the amount by which the labels should be scaled relative to the default. Ignored if lab is NULL.

Value

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

synopsis

atvnonpar(x = rep(1/3,3), data, nsloc1 = NULL, nsloc2 = NULL, nsloc3 = NULL, method = c("pickands", "deheuvels", "hall"), 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)

See Also

atvpar, 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)
atvnonpar(s3pts, sdat)

atvnonpar(data = sdat, plot = TRUE)
atvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
atvpar(dep = 0.6, model = "log", plot = TRUE)
atvpar(dep = 0.6, model = "log", plot = TRUE, blty = 1)