Distribution function and random generation for the
multivariate logistic distribution.
Usage
pmvlog(q, dep, d = 2, mar = c(1, 1, 0))
rmvlog(n, dep, d = 2, mar = c(1, 1, 0))
Arguments
q
a vector of length d or a matrix with d
columns, in which case the distribution is evaluated across
the rows.
n
number of observations.
dep
dependence parameter.
d
dimension.
mar
a vector of length three containing the marginal
parameters for every univariate margin.
Value
pmvlog gives the distribution function and rmvlog
generates random deviates.
Details
Let $z = (z_1,z_2,\ldots,z_d)$.
The d dimensional multivariate logistic distribution
function with parameter $\code{dep} = r$ is
$$G(z) = \exp\left[-(y_1^{1/r}+\ldots+y_d^{1/r})^r\right]$$
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
$i = 1,\ldots,d$.
Different parameters on each margin are not implemented, so
$\code{mar} = (a_i,b_i,s_i)$
for every $i$.
If $s_i = 0$ then $y_i$ is defined by continuity.
This is a special case of the multivariate asymmetric logistic
distribution.
The univariate marginal distributions are generalized extreme value.
References
Kotz, S. and Balakrishnan, N. and Johnson, N. L. (2000)
Continuous Multivariate Distributions, vol. 1.
New York: John Wiley & Sons, 2nd edn.
Stephenson, A. G. (2002)
Simulating multivariate extreme value distributions of logistic type.
To be published - available on request.