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Maximum likelihood estimation for scale-shape mixtures of flexible generalized skew normal distributions via selection representation

Author

Listed:
  • Abbas Mahdavi

    (Shahid Bahonar University of Kerman)

  • Vahid Amirzadeh

    (Shahid Bahonar University of Kerman)

  • Ahad Jamalizadeh

    (Shahid Bahonar University of Kerman)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

A scale-shape mixtures of flexible generalized skew normal (SSMFGSN) distributions is proposed as a novel device for modeling asymmetric data. Computationally feasible EM-type algorithms derived from the selection mechanism are presented to compute maximum likelihood (ML) estimates of SSMFGSN distributions. Some characterizations and probabilistic properties of the SSMFGSN distributions are also studied. Monte Carlo simulations show that the proposed estimating procedures can provide desirable asymptotic properties of the ML estimates and demand less computational burden in comparison with other existing algorithms based on convolution representations. The usefulness of the proposed methodology is illustrated by analyzing a real dataset.

Suggested Citation

  • Abbas Mahdavi & Vahid Amirzadeh & Ahad Jamalizadeh & Tsung-I Lin, 2021. "Maximum likelihood estimation for scale-shape mixtures of flexible generalized skew normal distributions via selection representation," Computational Statistics, Springer, vol. 36(3), pages 2201-2230, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01079-2
    DOI: 10.1007/s00180-021-01079-2
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    References listed on IDEAS

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    1. 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.
    2. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    3. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    4. Yanyuan Ma & Marc G. Genton, 2004. "Flexible Class of Skew‐Symmetric Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(3), pages 459-468, September.
    5. Arellano-Valle, Reinaldo B. & Ferreira, Clécio S. & Genton, Marc G., 2018. "Scale and shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 98-110.
    6. Wan-Lun Wang & Ahad Jamalizadeh & Tsung-I Lin, 2020. "Finite mixtures of multivariate scale-shape mixtures of skew-normal distributions," Statistical Papers, Springer, vol. 61(6), pages 2643-2670, December.
    7. 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.
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