A multivariate and asymmetric generalization of Laplace distribution
type: Item
instance of: scholarly article
title: A multivariate and asymmetric generalization of Laplace distribution
zbMATH Open document ID: 1035.60010
author: Tomasz J. Kozubowski
author: Krzysztof Podgórski
published in: Computational Statistics
publication date: 2004-03-16T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60E07
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 2058947
zbMATH Keywords: Laplace distribution
zbMATH Keywords: geometric distribution
zbMATH Keywords: Bessel function
zbMATH Keywords: geometric stable law
zbMATH Keywords: heavy tailed modelling
zbMATH Keywords: elliptically contoured distribution
zbMATH Keywords: mixture
zbMATH Keywords: random summation
zbMATH Keywords: simulation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2058947