Krzysztof Podgórski
Professor, Head of the Department of Statistics
Gaussian Mixture Representation of the Laplace Distribution Revisited : Bibliographical Connections and Extensions
Author
Summary, in English
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.
Department/s
- Department of Statistics
Publishing year
2020
Language
English
Pages
407-412
Publication/Series
American Statistician
Volume
74
Issue
4
Document type
Journal article (comment)
Publisher
Taylor & Francis
Topic
- Probability Theory and Statistics
Keywords
- Asymmetric Laplace distribution
- Bartlett decomposition
- Laplace Lévy motion
- Multivariate Laplace distribution
- Scale mixture
- Stochastic representation
Status
Published
ISBN/ISSN/Other
- ISSN: 0003-1305