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On Mean And/or Variance Mixtures of Normal Distributions

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Statistical Learning and Modeling in Data Analysis (CLADAG 2019)

Abstract

Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these distributions, focusing on those that are obtained by scaling the mean and/or covariance matrix of the (multivariate) normal distribution with some scaling variable(s). Namely, we consider the families of the mean mixture, variance mixture, and mean–variance mixture of normal distributions. Their basic properties, some notable special/limiting cases, and parameter estimation methods are also described.

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Author information

Authors and Affiliations

  1. University of Adelaide, Adelaide, Australia

    Sharon X. Lee

  2. University of Queensland, Brisbane, Australia

    Geoffrey J. McLachlan

Authors
  1. Sharon X. Lee
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  2. Geoffrey J. McLachlan
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Corresponding author

Correspondence to Sharon X. Lee .

Editor information

Editors and Affiliations

  1. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy

    Simona Balzano

  2. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy

    Giovanni C. Porzio

  3. Department of Economics and Law, University of Cassino and Southern Lazio, Cassino, Italy

    Renato Salvatore

  4. Department of Political Science, University of Naples Federico II, Naples, Italy

    Domenico Vistocco

  5. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maurizio Vichi

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Lee, S.X., McLachlan, G.J. (2021). On Mean And/or Variance Mixtures of Normal Distributions. In: Balzano, S., Porzio, G.C., Salvatore, R., Vistocco, D., Vichi, M. (eds) Statistical Learning and Modeling in Data Analysis. CLADAG 2019. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Cham. https://doi.org/10.1007/978-3-030-69944-4_13

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