IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i2d10.1007_s00180-016-0691-1.html
   My bibliography  Save this article

A general class of scale-shape mixtures of skew-normal distributions: properties and estimation

Author

Listed:
  • Ahad Jamalizadeh

    (Shahid Bahonar University of Kerman)

  • Tsung-I Lin

    (National Chung Hsing University
    China Medical University)

Abstract

This paper introduces the scale-shape mixtures of skew-normal (SSMSN) distributions which provide alternative candidates for modeling asymmetric data in a wide variety of settings. We obtain the moments and study some characterizations of the SSMSN distributions. Instead of resorting to numerical optimization procedures, two variants of EM algorithms are developed for carrying out maximum likelihood estimation. Our algorithms are analytically simple because closed-form expressions of conditional expectations in the E-step as well as the updating estimators in the M-step can be explicitly obtained. The observed information matrix is derived for approximating the asymptotic covariance matrix of parameter estimates. A simulation study is conducted to examine the finite sample properties of ML estimators. The utility of the proposed methodology is illustrated by analyzing a real example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0691-1
    DOI: 10.1007/s00180-016-0691-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-016-0691-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-016-0691-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. McLachlan, Geoff & Lee, Sharon X, 2013. "EMMIXuskew: An R Package for Fitting Mixtures of Multivariate Skew t Distributions via the EM Algorithm," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i12).
    2. -, 2003. "Capital flows to Latin America: first quarter 2003," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28822, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    3. 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.
    4. 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.
    5. -, 2003. "Capital flows to Latin America: second quarter 2002," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28812, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    6. Álvarez Alvarado, Marcos Tulio, 2003. "¿Existe una alternativa al capitalismo?," Observatorio de la Economía Latinoamericana, Servicios Académicos Intercontinentales SL. Hasta 31/12/2022, issue 16, November.
    7. Cabral, Celso Rômulo Barbosa & Bolfarine, Heleno & Pereira, José Raimundo Gomes, 2008. "Bayesian density estimation using skew student-t-normal mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5075-5090, August.
    8. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    9. Aldo M. Garay & Heleno Bolfarine & Victor H. Lachos & Celso R.B. Cabral, 2015. "Bayesian analysis of censored linear regression models with scale mixtures of normal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(12), pages 2694-2714, December.
    10. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    11. -, 2003. "Capital flows to Latin America: second quarter 2003," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28823, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    12. -, 2003. "Capital flows to Latin America: first quarter 2002," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28811, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    13. -, 2003. "Capital flows to Latin America: fourth quarter 2002," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28814, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    14. -, 2003. "Capital flows to Latin America: third quarter 2003," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28824, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    15. -, 2003. "Capital flows to Latin America: third quarter 2002," Oficina de la CEPAL en Washington (Estudios e Investigaciones) 28813, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. Hossein Negarestani & Ahad Jamalizadeh & Sobhan Shafiei & Narayanaswamy Balakrishnan, 2019. "Mean mixtures of normal distributions: properties, inference and application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 501-528, May.
    4. 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.
    5. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. McLachlan, Geoff & Lee, Sharon X, 2013. "EMMIXuskew: An R Package for Fitting Mixtures of Multivariate Skew t Distributions via the EM Algorithm," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i12).
    2. Mehdi Amiri & Ahad Jamalizadeh & Mina Towhidi, 2015. "Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution," Statistical Papers, Springer, vol. 56(4), pages 1071-1098, November.
    3. Komárek, Arnošt & Komárková, Lenka, 2014. "Capabilities of R Package mixAK for Clustering Based on Multivariate Continuous and Discrete Longitudinal Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 59(i12).
    4. Wan-Lun Wang & Min Liu & Tsung-I Lin, 2017. "Robust skew-t factor analysis models for handling missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 649-672, November.
    5. Tao Lu, 2017. "Bayesian inference on longitudinal-survival data with multiple features," Computational Statistics, Springer, vol. 32(3), pages 845-866, September.
    6. Wan-Lun Wang & Tsung-I Lin, 2015. "Robust model-based clustering via mixtures of skew-t distributions with missing information," 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. 9(4), pages 423-445, December.
    7. Yangxin Huang & Tao Lu, 2017. "Bayesian inference on partially linear mixed-effects joint models for longitudinal data with multiple features," Computational Statistics, Springer, vol. 32(1), pages 179-196, March.
    8. John Marangos & Charles J. Whalen, 2011. "Evolution without fundamental change: the Washington Consensus on economic development," Chapters, in: Charles J. Whalen (ed.), Financial Instability and Economic Security after the Great Recession, chapter 8, pages 153-178, Edward Elgar Publishing.
    9. Alvaro Cuervo-Cazurra & Luis Alfonso Dau, 2009. "Structural Reform and Firm Exports," Management International Review, Springer, vol. 49(4), pages 479-507, September.
    10. Tsung-I Lin & Pal Wu & Geoffrey McLachlan & Sharon Lee, 2015. "A robust factor analysis model using the restricted skew- $$t$$ t distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 510-531, September.
    11. Lee, Sharon X. & McLachlan, Geoffrey J., 2022. "An overview of skew distributions in model-based clustering," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    13. Catarina Figueira & David Parker, 2011. "Infrastructure Liberalization: Challenges to the New Economic Paradigm in the Context of Developing Countries," Chapters, in: Matthias Finger & Rolf W. Künneke (ed.), International Handbook of Network Industries, chapter 27, Edward Elgar Publishing.
    14. Matthias Finger & Rolf W. Künneke (ed.), 2011. "International Handbook of Network Industries," Books, Edward Elgar Publishing, number 12961.
    15. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    16. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    17. Joe, Harry & Li, Haijun, 2019. "Tail densities of skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 421-435.
    18. Maria Carolina Basso, 2016. "A Economia Brasileira Sob Restrição Do Balanço De Pagamentos: Uma Análise Empírica Da Lei De Thirlwall No Boom Das Commodities," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 089, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    19. Batiz-Zuk, Enrique & Christodoulakis, George & Poon, Ser-Huang, 2015. "Credit contagion in the presence of non-normal shocks," International Review of Financial Analysis, Elsevier, vol. 37(C), pages 129-139.
    20. Zinoviy Landsman & Udi Makov & Tomer Shushi, 2017. "Extended Generalized Skew-Elliptical Distributions and their Moments," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-100, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0691-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.