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

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  • Tomasz J. Kozubowski
  • Krzysztof Podgórski

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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  • Tomasz J. Kozubowski & Krzysztof Podgórski, 2020. "Gaussian Mixture Representation of the Laplace Distribution Revisited: Bibliographical Connections and Extensions," The American Statistician, Taylor & Francis Journals, vol. 74(4), pages 407-412, October.
    • Handle: RePEc:taf:amstat:v:74:y:2020:i:4:p:407-412
    DOI: 10.1080/00031305.2019.1630000
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    Cited by:

    1. Kozubowski, Tomasz J. & Mazur, Stepan & Podgorski, Krysztof, 2022. "Matrix Variate Generalized Laplace Distributions," Working Papers 2022:7, Örebro University, School of Business.

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