atvpar {evd} | R Documentation |
Calculate or plot the dependence function A for the trivariate logistic and trivariate asymmetric logistic models.
atvpar(x = rep(1/3,3), dep, asy, model = c("log", "alog"), 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)
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. |
dep |
The dependence parameter(s). For the logistic model,
should be a single value. For the asymmetric logistic model,
should be a vector of length four, or a single value,
in which case the value is used for each of the four
parameters (see rmvevd ). |
asy |
The asymmetry parameters for the asymmetric logistic
model. Should be a list with seven vector elements; three
of length one, three of length two and one of length three,
containing the asymmetry parameters for each separate component
(see rmvevd and Examples). |
model |
The specified model; a character string. Must be
either "log" (the default) or "alog" (or any unique
partial match), for the logistic and asymmetric logistic models
respectively. The definition of each model is given (for general
dimensions) in rmvevd . |
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
defualt 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
i th margin is labelled using the i th component,
or NULL , in which case no labels are given. 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 . |
Let z = (z1,z2,z3) and w = (w1,w2,w3). Any trivariate extreme value distribution can be written as
G(z) = exp{-(y1+y2+y3) A[y1/(y1+y2+y3),y2/(y1+y2+y3), y3/(y1+y2+y3)]}
for some function A defined on the simplex S_3 = {w: w1 + w2 + w3 = 1}, where
yi = {1+si(zi-ai)/bi}^(-1/si)
for 1+si(zi-ai)/bi > 0 and i = 1,2,3, and where the (generalized extreme value) marginal parameters are given by (ai,bi,si), bi > 0. If si = 0 then yi is defined by continuity.
A is called (by some authors) the dependence function. It follows that A(1,0,0) = A(0,1,0) = A(0,0,1) = 1, and that A is a convex function with max(w1,w2,w3) <= A(w) <= 1 for all w in S_3. The lower and upper limits of A are obtained under complete dependence and mutual independence respectively. A does not depend on the marginal parameters.
atvpar
calculates or plots the dependence function
for the trivariate logistic and trivariate asymmetric logistic
models, at specified parameter values.
atvnonpar
, abvpar
,
rmvevd
, image
atvpar(dep = 0.5, model = "log") s3pts <- matrix(rexp(30), nrow = 10, ncol = 3) s3pts <- s3pts/rowSums(s3pts) atvpar(s3pts, dep = 0.5, model = "log") ## Not run: atvpar(dep = 0.05, model = "log", plot = TRUE, blty = 1) atvpar(dep = 0.95, model = "log", plot = TRUE, lower = 0.94) asy <- list(.4, .1, .6, c(.3,.2), c(.1,.1), c(.4,.1), c(.2,.3,.2)) atvpar(s3pts, dep = 0.15, asy = asy, model = "alog") atvpar(dep = 0.15, asy = asy, model = "al", plot = TRUE, lower = 0.7)