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A flexible extension of skew generalized normal distribution

Author

Listed:
  • Mahdi Rasekhi

    (Malayer University)

  • G. G. Hamedani

    (Marquette University)

  • Rahim Chinipardaz

    (Shahid Chamran University of Ahvaz)

Abstract

We introduce an extension of the skew generalized normal distribution called shape-skew generalized normal distribution. The proposed distribution has certain type of flexibility which is different from those given in other flexible skew normal distributions. It possesses properties such as uni/bimodality, skewness, wider range of the Pearson’s excess kurtosis coefficient ( $$\gamma _{2}$$ γ 2 ) with respect to skew generalized normal distribution and preserving the most desirable features of the skew generalized normal distribution. Some basic distributional properties of the new extension including moments, moment generating function, characterization and relation to other distributions are derived. Also, the multivariate case of our proposed distribution is introduced and some of its properties are studied. The suitability of our model is demonstrated via comparisons with other generalized models.

Suggested Citation

  • Mahdi Rasekhi & G. G. Hamedani & Rahim Chinipardaz, 2017. "A flexible extension of skew generalized normal distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 87-107, April.
    • Handle: RePEc:spr:metron:v:75:y:2017:i:1:d:10.1007_s40300-017-0106-2
    DOI: 10.1007/s40300-017-0106-2
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    References listed on IDEAS

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    1. Behboodian, J. & Jamalizadeh, A. & Balakrishnan, N., 2006. "A new class of skew-Cauchy distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1488-1493, August.
    2. P. Hasanalipour & M. Sharafi, 2012. "A new generalized Balakrishnan skew-normal distribution," Statistical Papers, Springer, vol. 53(1), pages 219-228, February.
    3. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.
    4. C. Satheesh Kumar & M. R. Anusree, 2015. "On an Extended Version of Skew Generalized Normal Distribution and Some of its Properties," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 573-586, February.
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    Cited by:

    1. Ralph Vince, 2023. "Expectation and Optimal Allocations in Existential Contests of Finite, Heavy-Tail-Distributed Outcomes," Mathematics, MDPI, vol. 12(1), pages 1-25, December.

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