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Flexible Class of Skew‐Symmetric Distributions

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  • Yanyuan Ma
  • Marc G. Genton

Abstract

. We propose a flexible class of skew‐symmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and multimodality systematically. We present three illustrative examples for the fibreglass data, the simulated data from a mixture of two normal distributions and the Swiss bills data.

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  • 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.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:3:p:459-468
    DOI: 10.1111/j.1467-9469.2004.03_007.x
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    Cited by:

    1. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. 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.
    3. Juan Duarte & Guillermo Martínez-Flórez & Diego Ignacio Gallardo & Osvaldo Venegas & Héctor W. Gómez, 2023. "A Bimodal Extension of the Epsilon-Skew-Normal Model," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    4. David Elal-Olivero & Juan F. Olivares-Pacheco & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2020. "On Properties of the Bimodal Skew-Normal Distribution and an Application," Mathematics, MDPI, vol. 8(5), pages 1-16, May.
    5. Lysenko, Natalia & Roy, Parthanil & Waeber, Rolf, 2009. "Multivariate extremes of generalized skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 525-533, February.
    6. Kim, Hea-Jung, 2008. "A class of weighted multivariate normal distributions and its properties," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1758-1771, September.
    7. Isaac E. Cortés & Osvaldo Venegas & Héctor W. Gómez, 2022. "A Symmetric/Asymmetric Bimodal Extension Based on the Logistic Distribution: Properties, Simulation and Applications," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    8. Seokho Lee & Marc G. Genton & Reinaldo B. Arellano-Valle, 2010. "Perturbation of Numerical Confidential Data via Skew-t Distributions," Management Science, INFORMS, vol. 56(2), pages 318-333, February.
    9. Martin Binder, 2014. "Should evolutionary economists embrace libertarian paternalism?," Journal of Evolutionary Economics, Springer, vol. 24(3), pages 515-539, July.
    10. Ley, Christophe & Paindaveine, Davy, 2010. "On the singularity of multivariate skew-symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1434-1444, July.
    11. Hok Shing Kwong & Saralees Nadarajah, 2022. "A New Robust Class of Skew Elliptical Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1669-1691, September.
    12. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2014. "Mixtures of skew-t factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 326-335.
    13. Samuel Kotz & Donatella Vicari, 2005. "Survey of developments in the theory of continuous skewed distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 225-261.
    14. Guillermo Martínez-Flórez & Diego I. Gallardo & Osvaldo Venegas & Heleno Bolfarine & Héctor W. Gómez, 2021. "Flexible Power-Normal Models with Applications," Mathematics, MDPI, vol. 9(24), pages 1-15, December.
    15. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    16. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    17. Daan de Waal & Tristan Harris & Alta de Waal & Jocelyn Mazarura, 2022. "Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    18. J. Rosco & M. Jones & Arthur Pewsey, 2011. "Skew t distributions via the sinh-arcsinh transformation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 630-652, November.
    19. M. C. Jones, 2015. "Rejoinder," International Statistical Review, International Statistical Institute, vol. 83(2), pages 223-227, August.
    20. Adelchi Azzalini & Giuliana Regoli, 2012. "Some properties of skew-symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 857-879, August.
    21. Emilio Gómez-Déniz & Barry C. Arnold & José M. Sarabia & Héctor W. Gómez, 2021. "Properties and Applications of a New Family of Skew Distributions," Mathematics, MDPI, vol. 9(1), pages 1-18, January.
    22. Bufalo, Michele & NIGRI, ANDREA, 2024. "Trimodal extension based on the flexible generalized skew-normal distribution," OSF Preprints axu6g, Center for Open Science.
    23. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    24. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.

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