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Gaussian Mixture Representation of the Laplace Distribution Revisited : Bibliographical Connections and Extensions

Kozubowski, Tomasz J. and Podgórski, Krzysztof LU (2020) In American Statistician 74(4). p.407-412
Abstract

We provide bibliographical connections and extensions of several representations of the classical Laplace distribution, discussed recently in the study of Ding and Blitzstein. Beyond presenting relation to some previous results, we also include their skew as well as multivariate versions. In particular, the distribution of det Z, where Z is an n × n matrix of iid standard normal components, is obtained for an arbitrary integer n. While the latter is a scale mixture of Gaussian distributions, the Laplace distribution is obtained only in the case n = 2. Supplementary materials for this article are available online.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Asymmetric Laplace distribution, Bartlett decomposition, Laplace Lévy motion, Multivariate Laplace distribution, Scale mixture, Stochastic representation
in
American Statistician
volume
74
issue
4
pages
6 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85094859726
ISSN
0003-1305
DOI
10.1080/00031305.2019.1630000
language
English
LU publication?
yes
id
9109e487-f98f-4202-9be4-b8fe820514a6
date added to LUP
2020-11-17 09:34:48
date last changed
2022-04-19 02:08:50
@misc{9109e487-f98f-4202-9be4-b8fe820514a6,
  abstract     = {{<p>We provide bibliographical connections and extensions of several representations of the classical Laplace distribution, discussed recently in the study of Ding and Blitzstein. Beyond presenting relation to some previous results, we also include their skew as well as multivariate versions. In particular, the distribution of det Z, where Z is an n × n matrix of iid standard normal components, is obtained for an arbitrary integer n. While the latter is a scale mixture of Gaussian distributions, the Laplace distribution is obtained only in the case n = 2. Supplementary materials for this article are available online.</p>}},
  author       = {{Kozubowski, Tomasz J. and Podgórski, Krzysztof}},
  issn         = {{0003-1305}},
  keywords     = {{Asymmetric Laplace distribution; Bartlett decomposition; Laplace Lévy motion; Multivariate Laplace distribution; Scale mixture; Stochastic representation}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{407--412}},
  publisher    = {{Taylor & Francis}},
  series       = {{American Statistician}},
  title        = {{Gaussian Mixture Representation of the Laplace Distribution Revisited : Bibliographical Connections and Extensions}},
  url          = {{http://dx.doi.org/10.1080/00031305.2019.1630000}},
  doi          = {{10.1080/00031305.2019.1630000}},
  volume       = {{74}},
  year         = {{2020}},
}