Computational Statistics

, Volume 34, Issue 1, pp 323–347 | Cite as

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

  • Mostafa Tamandi
  • Ahad Jamalizadeh
  • Tsung-I LinEmail author
Original Paper


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.


Asymmetry ECME algorithm Observed information matrix Robustness Skew-symmetric Truncated normal 



We gratefully acknowledge the chief editor, the associate editor and two anonymous referees for their valuable comments and suggestions, which led to a greatly improved version of this article. This research was supported by MOST 105-2118-M-005-003-MY2 awarded by the Ministry of Science and Technology of Taiwan.

Supplementary material

180_2018_835_MOESM1_ESM.pdf (538 kb)
Supplementary material 1 (pdf 537 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Mostafa Tamandi
    • 1
  • Ahad Jamalizadeh
    • 1
  • Tsung-I Lin
    • 2
    • 3
    Email author
  1. 1.Department of Statistics, Faculty of Mathematics & ComputerShahid Bahonar University of KermanKermanIran
  2. 2.Institute of StatisticsNational Chung Hsing UniversityTaichungTaiwan
  3. 3.Department of Public HealthChina Medical UniversityTaichungTaiwan

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