A multivariate and asymmetric generalization of Laplace distribution (Q1424609)

The authors describe the class of multivariate and not necessarily symmetric distributions called asymmetric Laplace (AL) laws that naturally extend properties and reduce to Laplace distribution in one dimension. Explicit forms of characteristic functions and densities of AL laws are presented, their properties are discussed, a representation that leads to a simple simulation method is derived. It is proved that AL class coincides with the class of limiting distributions as \(p\to\infty\) in the random summation scheme \(\sqrt{(p)}\sum_{i=1}^{N_p}(y_i+(\sqrt{(p)}-1)m)\), where \(\{y_i,i\geq 1\}\) are i.i.d. random vectors in \(R^d\) with the mean vector \(m\) and finite second moments, \(N_p\) is a geometrically distributed random variable independent of \(\{y_i,i\geq 1\}\). Relations to other formerly considered classes of distributions containing Laplace laws are discussed.