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.
asy
a vector containing the two asymmetry parameters.
mar1, mar2
vectors of length three containing marginal
parameters.
log
logical; if TRUE, the log density is returned.
Value
dbvalog gives the density, pbvalog gives the
distribution function and rbvalog generates random deviates.
Details
The bivariate asymmetric logistic distribution function with
parameters $\code{dep} = r$ and
$\code{asy} = (t_1,t_2)$ is
$$G(z_1,z_2) = \exp\left{-(1-t_1)y_1-(1-t_2)y_2-
[(t_1y_1)^{1/r}+(t_2y_2)^{1/r}]^r\right}$$
where $0 < r \leq 1$,
$0 \leq t_1,t_2 \leq 1$, 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.
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.