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Inference and further probabilistic properties of the $$ SUN_{n,2}$$ S U N n , 2 -distribution

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  • Mehdi Amiri
  • Ahad Jamalizadeh
  • Mina Towhidi

Abstract

In this paper the normal-skew-normal distribution, proposed by Gomez et al. (Statistics 47:411–421, 2013 ), is extended to the multivariate case. It is also a special case of $$SUN_{n,2}$$ S U N n , 2 -distribution, recently studied by Arellano-Valle and Genton (Chil J Stat 2:17–34, 2010 ). We show that the proposed distribution can be expressed as a shape mixture of the multivariate extended skew-normal distribution. Applying this property leads to deriving stochastic representations for the proposed distribution. Also we give some basic properties for this new family. Computational techniques using EM-type algorithms are employed for iteratively computing maximum likelihood estimates. Finally, an application of the new distribution is illustrated using some real data sets. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:4:p:1071-1098
    DOI: 10.1007/s00362-014-0625-3
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    1. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Balakrishnan, N. & Scarpa, Bruno, 2012. "Multivariate measures of skewness for the skew-normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 73-87, February.
    3. -, 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).
    4. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    5. Monica Chiogna, 1998. "Some results on the scalar Skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 7(1), pages 1-13, April.
    6. -, 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).
    7. -, 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).
    8. Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
    9. ., 1999. "The assessment of capital adequacy," Chapters, in: Handbook of Banking Regulation and Supervision in the United Kingdom, chapter 17, Edward Elgar Publishing.
    10. -, 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).
    11. 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.
    12. 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.
    13. 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.
    14. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.
    15. Huang, Wen-Jang & Chen, Yan-Hau, 2006. "Quadratic forms of multivariate skew normal-symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 76(9), pages 871-879, May.
    16. -, 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).
    17. -, 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).
    18. Rahman, M.M & Munsur, M.A.Z, 2009. "Genetic divergence analysis of lime," Journal of the Bangladesh Agricultural University, Bangladesh Agricultural University Research System (BAURES), vol. 7.
    19. -, 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).
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