abvevd {evd} | R Documentation |
Calculate or plot the dependence function A for nine parametric bivariate extreme value models.
abvevd(x = 0.5, dep, asy = c(1,1), alpha, beta, model = "log", rev = FALSE, plot = FALSE, add = FALSE, lty = 1, lwd = 1, col = 1, blty = 3, blwd = 1, xlim = c(0,1), ylim = c(0.5,1), xlab = "t", ylab = "A(t)", ...)
x |
A vector of values at which the dependence function is
evaluated (ignored if plot or add is TRUE ). A(1/2)
is returned by default since it is often a useful summary of
dependence. |
dep |
Dependence parameter for the logistic, asymmetric logistic, Husler-Reiss, negative logistic and asymmetric negative logistic models. |
asy |
A vector of length two, containing the two asymmetry parameters for the asymmetric logistic and asymmetric negative logistic models. |
alpha, beta |
Alpha and beta parameters for the bilogistic, negative bilogistic, Coles-Tawn and asymmetric mixed models. |
model |
The specified model; a character string. Must be
either "log" (the default), "alog" , "hr" ,
"neglog" , "aneglog" , "bilog" ,
"negbilog" , "ct" or "amix" (or any unique
partial match), for the logistic, asymmetric logistic,
Husler-Reiss, negative logistic, asymmetric negative logistic,
bilogistic, negative bilogistic, Coles-Tawn and asymmetric
mixed models respectively. The definition of each model is given
in rbvevd . If parameter arguments are given that do
not correspond to the specified model those arguments are
ignored, with a warning. |
rev |
Logical; reverse the dependence function? This is
equivalent to evaluating the function at 1-x . |
plot |
Logical; if TRUE the function is plotted. The
x and y values used to create the plot are returned invisibly.
If plot and add are FALSE (the default),
the arguments following add are ignored. |
add |
Logical; add to an existing plot? The existing plot
should have been created using either abvevd or
abvnonpar , the latter of which plots (or calculates)
a non-parametric estimate of the dependence function. |
lty, blty |
Function and border line types. Set blty
to zero to omit the border. |
lwd, blwd |
Function an border line widths. |
col |
Line colour. |
xlim, ylim |
x and y-axis limits. |
xlab, ylab |
x and y-axis labels. |
... |
Other high-level graphics parameters to be passed to
plot . |
Any bivariate extreme value distribution can be written as
G(z1,z2) = exp{-(y1+y2)A[y1/(y1+y2)]}
for some function A() defined on [0,1], where
yi = {1+si(zi-ai)/bi}^(-1/si)
for 1+si(zi-ai)/bi > 0 and i = 1,2, with the (generalized extreme value) marginal parameters 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(0)=A(1)=1, and that A() is a convex function with max(x,1-x) <= A(x) <= 1 for all 0 <= x <= 1. The lower and upper limits of A are obtained under complete dependence and independence respectively. A() does not depend on the marginal parameters.
Some authors take B(x) = A(1-x) as the dependence function. If the
argument rev = TRUE
, then B(x) is plotted/evaluated.
abvevd
calculates or plots the dependence function
for one of nine parametric bivariate extreme value models,
at specified parameter values.
abvnonpar
, fbvevd
,
rbvevd
, amvevd
abvevd(dep = 2.7, model = "hr") abvevd(seq(0,1,0.25), dep = 0.3, asy = c(.7,.9), model = "alog") abvevd(alpha = 0.3, beta = 1.2, model = "negbi", plot = TRUE) bvdata <- rbvevd(100, dep = 0.7, model = "log") M1 <- fitted(fbvevd(bvdata, model = "log")) abvevd(dep = M1["dep"], model = "log", plot = TRUE) abvnonpar(data = bvdata, add = TRUE, lty = 2)