Gaussian Mixture Representation of the Laplace Distribution Revisited : Bibliographical Connections and Extensions
(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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https://lup.lub.lu.se/record/9109e487-f98f-4202-9be4-b8fe820514a6
- author
- Kozubowski, Tomasz J. and Podgórski, Krzysztof LU
- organization
- publishing date
- 2020
- 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}}, }