A multivariate generalized Laplace distributions design. (English) Zbl 0922.62043
A class of p-variate generalized Laplace distributions is defined as a class of distributions with density functions of the form
\[
f(x)= K_{p,\lambda}| \Sigma| ^{-1/2}\exp\{-[(x-m)^{'}\Sigma^{-1}(x-m)]^{\lambda/2}\},
\]
where vector \(m\in R^p\), \(\Sigma\) is \(p\times p\) symmetric positive definite matrix, \(p\geq 2\), and \(\lambda >0\). This class includes multivariate versions of the normal, Laplace and uniform distributions and has deep interrelations with elliptically contoured distributions. A method of simulation is described and certain bivariate density plots are given.
Reviewer: N.M.Zinchenko (Kyïv)
MSC:
62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
62H10 | Multivariate distribution of statistics |
60E99 | Distribution theory |
65C05 | Monte Carlo methods |