Proyecciones Journal of Mathematics Vol. 30, N^o 3, pp. 401-413, December 2011. Universidad Católica del Norte Antofagasta - Chile

 

An extension of the skew-generalized normal distribution and its derivation

Osvaldo Venegas

Universidad Catolica de Temuco, Chile

Antonio I. Sanhueza

Universidad de La Frontera, Chile

Héctor W. Gómez

Universidad de Antofagasta, Chile

 

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ABSTRACT

In this paper, we introduce a new class of skew-symmetric distributions which are formulated based on cumulative distributions of skew-symmetric densities. This new class is an extension of other skew-symmetric distributions that have already been studied. We give special attention to a family from this class that could be seen as an extension ofthe skew-generalized-normal model introduced by Arellano-Valle et al.(2004). We study the main properties, stochastic representation, moments and an extension of this new model.

Keywords : Asymmetry; Skew-Generalized Normal Distribution; Skew-Normal Distribution.

 

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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 Statistics : Theory and Methods, 33(7), pp. 1465—1480, (2004).

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[9] Martinez, E., Varela, H., Gómez, H. W. and Bolfarine, H. A note on the likelihood and moments of the skew-normal distribution. Statistics and Operations Research Transactions (SORT). 32(1), pp. 57-66, (2008).

[10] Nadarajah, S., Kotz, S. Skewed distributions generated by the normal kernel. Statistics Probability Letters, 65, pp. 269—277, (2003).

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Osvaldo Venegas

Departamento de Cs. Matematicas y Fisicas, Facultad de Ingenieria, Universidad Catolica de Temuco,

Chile

e-mail : ovenegas@uct.cl

 

Antonio I. Sanhueza

Departamento de Matematica y Estadistica, Facultad de Ingenieria, Ciencias y Administracion, Universidad de La Frontera,

Chile

e-mail : asanhue@ufro.cl

 

Héctor W. Gómez

Departamento de Matematicas, Facultad de Ciencias Basicas, Universidad de Antofagasta,

Chile

e-mail: hgomez@uantof.cl

 

Received : October 2010. Accepted : September 2011