a vector of length two or a matrix with two columns,
in which case the density/distribution is evaluated across
the rows.
n
number of observations.
dep
dependence parameter.
mar1, mar2
vectors of length three containing marginal
parameters.
log
logical; if TRUE, the log density is returned.
Value
dbvhr gives the density, pbvhr gives the
distribution function and rbvhr generates random deviates.
Details
The Husler-Reiss distribution function with parameter
$\code{dep} = r$ is
$$G(z_1,z_2) = \exp\left(-y_1\Phi{r^{-1}+{\textstyle\frac{1}{2}}
r[\log(y_1/y_2)]} - y_2\Phi{r^{-1}+{\textstyle\frac{1}{2}}r
[\log(y_2/y_1)]}\right)$$
where $\Phi(\cdot)$ is the standard normal distribution
function, $r > 0$ and
$$y_i = {1+s_i(z_i-a_i)/b_i}^{-1/s_i}$$
for $1+s_i(z_i-a_i)/b_i > 0$ and
$i = 1,2$, where the marginal
parameters are given by
$\code{mari} = (a_i,b_i,s_i)$,
$b_i > 0$.
If $s_i = 0$ then $y_i$ is defined by
continuity.
The univariate marginal distributions are generalized extreme
value.