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Bimodal skew-symmetric normal distribution

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  • M.Y. Hassan
  • M.Y. El-Bassiouni

Abstract

We introduce a new parsimonious bimodal distribution, referred to as the bimodal skew-symmetric Normal (BSSN) distribution, which is potentially effective in capturing bimodality, excess kurtosis, and skewness. Explicit expressions for the moment-generating function, mean, variance, skewness, and excess kurtosis were derived. The shape properties of the proposed distribution were investigated in regard to skewness, kurtosis, and bimodality. Maximum likelihood estimation was considered and an expression for the observed information matrix was provided. Illustrative examples using medical and financial data as well as simulated data from a mixture of normal distributions were worked.

Suggested Citation

  • M.Y. Hassan & M.Y. El-Bassiouni, 2016. "Bimodal skew-symmetric normal distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1527-1541, March.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:5:p:1527-1541
    DOI: 10.1080/03610926.2014.882950
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    Cited by:

    1. Mehmet Niyazi Çankaya & Abdullah Yalçınkaya & Ömer Altındaǧ & Olcay Arslan, 2019. "On the robustness of an epsilon skew extension for Burr III distribution on the real line," Computational Statistics, Springer, vol. 34(3), pages 1247-1273, September.
    2. Juan Duarte & Guillermo Martínez-Flórez & Diego Ignacio Gallardo & Osvaldo Venegas & Héctor W. Gómez, 2023. "A Bimodal Extension of the Epsilon-Skew-Normal Model," Mathematics, MDPI, vol. 11(3), pages 1-18, January.

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