Description Usage Arguments Details Value Point Masses See Also Examples
Calculate or plot the density h of the spectral measure H on the interval (0,1), for nine parametric bivariate extreme value models.
1 2 3 
x 
A vector of values at which the function is evaluated
(ignored if plot or add is 
dep 
Dependence parameter for the logistic, asymmetric logistic, HuslerReiss, 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, ColesTawn and asymmetric mixed models. 
model 
The specified model; a character string. Must be
either 
half 
Logical; if 
plot 
Logical; if 
add 
Logical; add to an existing plot? 
lty 
Line type. 
... 
Other highlevel graphics parameters to be passed to

Any bivariate extreme value distribution can be written as
G(z1,z2) = exp{\int_0^1 max(w y1, (1w) y2) H(dw)}
for some function H() defined on [0,1], satisfying
\int_0^1 w H(dw) = int_0^1 (1w) H(dw) = 1.
In particular, the total mass of H is two.
The functions y1 and y2 are as defined in
abvevd
.
H is called the spectral measure, with density h on the interval (0,1).
hbvevd
calculates or plots the spectral density function
h for one of nine parametric bivariate extreme value models,
at specified parameter values.
For differentiable models H may have up to two point masses:
at zero and one. Assuming that the model parameters are in the
interior of the parameter space, we have the following. For the
asymmetric logistic and asymmetric negative logistic models the
point masses are of size 1asy1
and 1asy2
respectively. For the asymmetric mixed model they are of size
1alphabeta
and 1alpha2*beta
respectively. For
all other models the point masses are zero.
At independence, H has point masses of size one at both zero and one. At complete dependence [a nondifferentiable model] H has a single point mass of size two at 1/2. In either case, h is zero everywhere.
abvevd
, fbvevd
,
rbvevd
, plot.bvevd
1 2 3 4 5 6 7  hbvevd(dep = 2.7, model = "hr")
hbvevd(seq(0.25,0.5,0.75), dep = 0.3, asy = c(.7,.9), model = "alog")
hbvevd(alpha = 0.3, beta = 1.2, model = "negbi", plot = TRUE)
bvdata < rbvevd(100, dep = 0.7, model = "log")
M1 < fitted(fbvevd(bvdata, model = "log"))
hbvevd(dep = M1["dep"], model = "log", plot = TRUE)

[1] 4.02297
[1] 1.8749
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