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Shape mixtures of skew-t-normal distributions: characterizations and estimation

Author

Listed:
  • Mostafa Tamandi

    (Shahid Bahonar University of Kerman)

  • Ahad Jamalizadeh

    (Shahid Bahonar University of Kerman)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

This paper introduces the shape mixtures of the skew-t-normal distribution which is a flexible extension of the skew-t-normal distribution as it contains one additional shape parameter to regulate skewness and kurtosis. We study some of its main characterizations, showing in particular that it is generated through a mixture on the shape parameter of the skew-t-normal distribution when the mixing distribution is normal. We develop an Expectation Conditional Maximization Either algorithm for carrying out maximum likelihood estimation. The asymptotic standard errors of estimators are obtained via the information-based approximation. The numerical performance of the proposed methodology is illustrated through simulated and real data examples.

Suggested Citation

  • Mostafa Tamandi & Ahad Jamalizadeh & Tsung-I Lin, 2019. "Shape mixtures of skew-t-normal distributions: characterizations and estimation," Computational Statistics, Springer, vol. 34(1), pages 323-347, March.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0835-6
    DOI: 10.1007/s00180-018-0835-6
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    References listed on IDEAS

    as
    1. Eling, Martin, 2014. "Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 45-56.
    2. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    3. Wan-Lun Wang & Tsung-I Lin, 2013. "An efficient ECM algorithm for maximum likelihood estimation in mixtures of t-factor analyzers," Computational Statistics, Springer, vol. 28(2), pages 751-769, April.
    4. Ahad Jamalizadeh & Tsung-I Lin, 2017. "A general class of scale-shape mixtures of skew-normal distributions: properties and estimation," Computational Statistics, Springer, vol. 32(2), pages 451-474, June.
    5. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
    6. Christopher Adcock & Martin Eling & Nicola Loperfido, 2015. "Skewed distributions in finance and actuarial science: a review," The European Journal of Finance, Taylor & Francis Journals, vol. 21(13-14), pages 1253-1281, November.
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    Cited by:

    1. Rocío Maehara & Heleno Bolfarine & Filidor Vilca & N. Balakrishnan, 2021. "A robust Birnbaum–Saunders regression model based on asymmetric heavy-tailed distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1049-1080, October.
    2. Uchenna Chinedu Nduka, 2022. "Efficient and robust estimation for autoregressive regression models using shape mixtures of skewt normal distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1519-1551, September.
    3. Fatma Zehra Doğru & Olcay Arslan, 2021. "Finite mixtures of skew Laplace normal distributions with random skewness," Computational Statistics, Springer, vol. 36(1), pages 423-447, March.

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