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Portrait of Krzysztof Podgórski. Photo.

Krzysztof Podgórski

Professor, Head of the Department of Statistics

Portrait of Krzysztof Podgórski. Photo.

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

Author

  • Tomasz J. Kozubowski
  • Krzysztof Podgórski

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