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The Multivariate Extended Skew Normal Distribution and Its Quadratic Forms

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Causal Inference in Econometrics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 622))

Abstract

In this paper, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, and independence are discussed. Based on this class of distributions, the extended noncentral skew chi-square distribution is defined and its properties are investigated. Also the necessary and sufficient conditions, under which a quadratic form of the model has an extended noncentral skew chi-square distribution, are obtained. For illustration of our main results, several examples are given.

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Author information

Authors and Affiliations

  1. Department Mathematical Sciences, New Mexico State University, Las Cruces, NM, USA

    Weizhong Tian, Cong Wang & Tonghui Wang

  2. College of Applied Sciences, Beijing University of Technology, Beijing, 100022, China

    Mixia Wu

Authors
  1. Weizhong Tian
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  2. Cong Wang
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  3. Mixia Wu
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  4. Tonghui Wang
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Corresponding author

Correspondence to Tonghui Wang .

Editor information

Editors and Affiliations

  1. School of Knowledge Science, Japan Advanced Ins. of Sci. & Tech, Ishikawa, Japan

    Van-Nam Huynh

  2. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  3. Faculty of Economics, Chiang Mai University, Chiangmai, Thailand

    Songsak Sriboonchitta

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Tian, W., Wang, C., Wu, M., Wang, T. (2016). The Multivariate Extended Skew Normal Distribution and Its Quadratic Forms. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S. (eds) Causal Inference in Econometrics. Studies in Computational Intelligence, vol 622. Springer, Cham. https://doi.org/10.1007/978-3-319-27284-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-27284-9_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27283-2

  • Online ISBN: 978-3-319-27284-9

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