abvpar {evd} | R Documentation |
Calculate or plot the dependence function A for eight parametric bivariate extreme value models.
abvpar(x = 0.5, dep, asy = c(1,1), alpha, beta, model = "log", plot = FALSE, add = FALSE, lty = 1, lwd = 1, col = 1, blty = 3, xlim = c(0,1), ylim = c(0.5,1), xlab = "", ylab = "", ...)
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 and Coles-Tawn models. |
model |
The specified model; a character string. Must be
either "log" (the default), "alog" , "hr" ,
"neglog" , "aneglog" , "bilog" ,
"negbilog" or "ct" (or any unique partial match),
for the logistic, asymmetric logistic, Husler-Reiss, negative
logistic, asymmetric negative logistic, bilogistic, negative
bilogistic and Coles-Tawn 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. |
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 abvpar 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 |
Line width. |
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.
abvpar
calculates or plots the dependence function
for one of eight parametric bivariate extreme value models,
at specified parameter values.
abvnonpar
, fbvevd
,
rbvevd
, atvpar
abvpar(dep = 2.7, model = "hr") abvpar(seq(0,1,0.25), dep = 0.3, asy = c(.7,.9), model = "alog") abvpar(alpha = 0.3, beta = 1.2, model = "negbi", plot = TRUE) bvdata <- rbvevd(100, dep = 0.7, model = "log") M1 <- fitted(fbvevd(bvdata, model = "log")) abvpar(dep = M1["dep"], model = "log", plot = TRUE) abvnonpar(data = bvdata, add = TRUE, lty = 2)