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Generalized elliptical distributions

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  • M. Arashi
  • S. Nadarajah

Abstract

A family of distributions generated by an operator acting on generalized normal density is introduced. This family contains as particular cases many known distributions, including the generalized normal, generalized t, and generalized gamma distributions. Several mathematical properties of the family (including expansions, characteristic function, moments, cumulants, and order statistics properties) are derived. Estimation procedures are derived too by the method of moments, method of maximum likelihood, and the method of empirical characteristic function. A real data application is presented. Finally, extensions to the multivariate case are outlined.

Suggested Citation

  • M. Arashi & S. Nadarajah, 2017. "Generalized elliptical distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6412-6432, July.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:13:p:6412-6432
    DOI: 10.1080/03610926.2015.1129415
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    Cited by:

    1. Matthias Wagener & Andriette Bekker & Mohammad Arashi, 2021. "Mastering the Body and Tail Shape of a Distribution," Mathematics, MDPI, vol. 9(21), pages 1-22, October.
    2. Danilo Leal & Rodrigo Jiménez & Marco Riquelme & Víctor Leiva, 2023. "Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale," Mathematics, MDPI, vol. 11(6), pages 1-27, March.

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