abvevd | 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 = c("log", "alog",
"hr", "neglog", "aneglog", "bilog", "negbilog", "ct", "amix"),
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 |
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 |
rev |
Logical; reverse the dependence function? This is
equivalent to evaluating the function at |
plot |
Logical; if |
add |
Logical; add to an existing plot? The existing plot
should have been created using either |
lty , blty |
Function and border line types. Set |
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
|
Any bivariate extreme value distribution can be written as
G(z_1,z_2) = \exp\left[-(y_1+y_2)A\left(
\frac{y_1}{y_1+y_2}\right)\right]
for some function A(\cdot)
defined on [0,1]
, where
y_i = \{1+s_i(z_i-a_i)/b_i\}^{-1/s_i}
for 1+s_i(z_i-a_i)/b_i > 0
and
i = 1,2
, with the (generalized extreme value) marginal
parameters given by (a_i,b_i,s_i)
,
b_i > 0
.
If s_i = 0
then y_i
is defined by
continuity.
A(\cdot)
is called (by some authors) the dependence
function.
It follows that A(0)=A(1)=1
, and that A(\cdot)
is
a convex function with \max(x,1-x) \leq A(x)\leq 1
for all 0\leq x\leq1
.
The lower and upper limits of A
are obtained under complete
dependence and independence respectively.
A(\cdot)
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)
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