Proyecciones Journal of Mathematics Vol. 31, N^o 3, pp. 197-207, September 2012. Universidad Católica del Norte Antofagasta - Chile

 

A note on rescalings of the skew-normal distribution

 

Osvaldo Venegas
Universidad Católica de Temuco, Chile

David Elal-Olivero
Universidad de Atacama, Chile

Héctor W. Gómez
Universidad de Antofagasta, Chile

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ABSTRACT

In this article, we show that certain skew-normal parametric statistical models are a result of rescalings of the skew normal model studied by Azzalini (1985). Using this procedure we define a class of skew-normal distributions and we study its moment, skewness and kurtosis coefficients. At the end of this article we will use this class of distribution to make some extensions of the skew-normal model.

Key Words : Asymmetry, Rescalings, Skew-Normal model.

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REFERENCES

[1] Arellano-Valle, R. B., Gómez, H. W. and Quintana, F. A. A New Class of Skew-Normal Distributions. Communications in Statististics: Theory and Methods. 33(7), pp. 1465-1480, (2004).         [ Links ]

[2] Azzalini, A. A class of distributions which includes the normal ones. Scand. J. Statist. 12, pp. 171-178, (1985).         [ Links ]

[3] Azzalini, A. Further results on a class of distributions which includes the normal ones. Statistica. 46, pp. 199-208, (1986).         [ Links ]

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[5] Henze, N. A probabilistic representation of the skew-normal distribution. Scand. J. Statist. 13, pp. 271-275, (1986).         [ Links ]

[6] Johnson, N., Kotz, S. L. and Balakrishann, N. Continuous univariate distributions, Second Edition. New York: Willey and Sons, (1995).         [ Links ]

[7] Mukhopadhyay, S. and Vidakovic, B. Efficiency of Linear Bayes Rules for a Normal Mean : Skewed Priors Class. The Statistician. 44 (3), p.389-397, (1995).         [ Links ]

[8] Nadarajah, N., Kotz, S. Skewed distributions generated by the normal kernel. Statistic & Probability Letters. 65, pp. 269-277, (2003).         [ Links ]

[9] Sahu, S. K., Dey, D. K. and Branco, M. A new class of multivariate skew distributions with application to Bayesian regression models. Canad. J.Statist. 31, pp. 129-150, (2003).         [ Links ]

 

Osvaldo Venegas

Departamento de Ciencias Matemóticas y Físicas, Facultad de Ingeniería, Universidad Catóolica de Temuco,

Chile,

e-mail: ovenegas@uct.cl

 

David Elal-Olivero

Departamento de Matemótica, Facultad de Ingeniería, Universidad de Atacama, Avenida Copayapu 485, Copiapóo,

Chile,

e-mail: delal@mat.uda.cl and

Hector W. Gomez

Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta,

Chile,

e-mail: hgomez@uantof.cl

 

Received : December 2011. Accepted : March 2012

Supported by Grant DGIP 2009 | 2 | 1. ,Grant DIUDA-221189 and FONDECYT (Chile) 1090411.