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
dbvlog gives the density, pbvlog gives the
distribution function and rbvlog generates random deviates.
Details
The bivariate logistic distribution function with
parameter $\code{dep} = r$ is
$$G(z_1,z_2) = \exp\left[-(y_1^{1/r}+y_2^{1/r})^r\right]$$
where $0 < r \leq 1$ 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.
This is a special case of the bivariate asymmetric logistic
distribution.
The univariate marginal distributions are generalized extreme
value.
References
Stephenson, A. G. (2002)
Simulating multivariate extreme value distributions of logistic type.
To be published - available on request.