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On the identifiability of finite mixture of Skew-Normal and Skew-t distributions

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  • Otiniano, C.E.G.
  • Rathie, P.N.
  • Ozelim, L.C.S.M.

Abstract

In this paper, the class of all finite mixtures of skew-normal distributions is proved to be identifiable. Also, the class of all finite mixtures of Skew-t distributions with null location parameter is proved to be identifiable. In order to achieve the results, the real moments of a Skew-t random variable are explicitly obtained in a closed-form. The latter is given in terms of the Meijer G-function.

Suggested Citation

  • Otiniano, C.E.G. & Rathie, P.N. & Ozelim, L.C.S.M., 2015. "On the identifiability of finite mixture of Skew-Normal and Skew-t distributions," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 103-108.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:103-108
    DOI: 10.1016/j.spl.2015.07.015
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    References listed on IDEAS

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    1. N. Atienza & J. Garcia-Heras & J. Muñoz-Pichardo, 2006. "A new condition for identifiability of finite mixture distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 215-221, April.
    2. Kim, Hyoung-Moon & Mallick, Bani K., 2003. "Moments of random vectors with skew t distribution and their quadratic forms," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 417-423, July.
    3. Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.
    4. Kim, Hyoung-Moon & Genton, Marc G., 2011. "Characteristic functions of scale mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1105-1117, August.
    5. Chan, Yin & Li, Haijun, 2008. "Tail dependence for multivariate t -copulas and its monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 763-770, April.
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    Cited by:

    1. Haas, Markus, 2016. "A note on optimal portfolios under regime–switching," Finance Research Letters, Elsevier, vol. 19(C), pages 209-216.
    2. Rendao Ye & Bingni Fang & Weixiao Du & Kun Luo & Yiting Lu, 2022. "Bootstrap Tests for the Location Parameter under the Skew-Normal Population with Unknown Scale Parameter and Skewness Parameter," Mathematics, MDPI, vol. 10(6), pages 1-23, March.
    3. Qi, Xuefei & Xu, Xingbai & Feng, Zhenghui & Peng, Heng, 2025. "Component selection and variable selection for mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 206(C).
    4. Libin Jin & Shuyan Chen & Xiaowen Dai & Lei Shi, 2025. "A penalized likelihood estimation for mixture regressions with skew-normal errors," Statistical Papers, Springer, vol. 66(6), pages 1-21, October.

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