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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.29 n.3 Antofagasta dic. 2010

http://dx.doi.org/10.4067/S0716-09172010000300006 

Proyecciones Journal of Mathematics
Vol. 29, N° 3, pp. 224-240, December 2010.
Universidad Católica del Norte
Antofagasta - Chile


ALPHA-SKEW-NORMAL DISTRIBUTION *


David Elal-Olivero


Universidad de Atacama, Chile



Correspondencia a:


Abstract

The main object of this paper is to introduce an alternative form of generate asymmetry in the normal distribution that allows to fit unimodal and bimodal data sets. Basic properties of this new distribution, such as stochastic representation, moments, maximum likelihood and the singularity of the Fisher information matrix are studied. The methodology developed is illustrated with a real application.

Keywords : Asymmetry; Bimodality; Skew-normal distribution; Stochastic representation; Maximum likelihood estimation; Singular information matrix



References

[1] Arellano-Valle, R. B., G´omez, 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).        [ Links ]

[2] Arellano-Valle, R. B., G´omez, H.W. and Quintana, F. A. Statistical inference for a general class of asymmetric distributions. Journal of Statistical Planning and Inference: 128(2), pp. 427 - 443, (2005).        [ Links ]

[3] Azzalini, A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics: 12, pp. 171-178, (1985).        [ Links ]

[4] Azzalini, A. Further results on a class of distributions which includes the normal ones. Statistica: 46(2), pp. 199-208, (1986).        [ Links ]

[5] Azzalini, A. and Capitonio A. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society series B: 65(2), pp. 367 - 389, (2003).        [ Links ]

[6] Chiogna, M. A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution. Statistical Methods and Applications: 14, pp. 331-341, (2005).        [ Links ]

[7] DiCiccio,T. J. and Monti, A. C. Inferencial Aspects of the Skew Exponcial Power Distribution. Journal of the American Statistical Association: 99(466), pp. 439-450, (2004).        [ Links ]

[8] Elal - Olivero, D., G´omez, H. W. and Quintana, F. A. Bayesian modeling using a class of bimodal skew-elliptical distributions. Journal of Statistical Planning and Inference: 139, pp. 1484-1492, (2009).        [ Links ]

[9] Genton, M. G., Ed. Skew-elliptical distributions and their applications : a journey beyond normality. Chapman & Hall/CRC, (2004).        [ Links ]

[10] Gomez H. ., Salinas, H. S. and Bolfarine, H. Generalized skew-normal models: Properties and Inference. Statistic: 40(6), pp. 495-505, (2006).        [ Links ]

[11] Henze, N. A probabilistic representation of the skew-normal distribution. Scandinavian Journal of Statistics: 13, pp. 271-275, (1986).        [ Links ]

[12] Ma Y. and Genton M, G. Flexible Class of Skew-Symmetric Distribution. Scandinavian Journal of Statistics: 31, pp. 459 - 468, (2004).        [ Links ]

[13] Mudholkar G.S. and Hutson, A. D. The epsilon-skew-normal distribution for analysing near-normal data. Journal of Statistical Planning and Inference: 83, pp. 291-309, (2000).        [ Links ]

[14] Pewsey, A. Problems of inference for Azzalini´s skew-normal distribution. Journal of Applied Statistics,Vol. 27, No:7, pp. 859-870, (2000).        [ Links ]

[15] Rotnitzky, A. Cox, D. R.,Bottai, M. and Robins, J. Likelihood - based inference with singular information matrix. Bernoulli: 6(2), pp. 243-284, (2000).        [ Links ]

[16] Salinas, H. S., Arellano-Valle, R. B. and G´omez H. W. The extended skew-exponencial power distribution and its derivations. Communications in Statistics : Theory and Methods: 36(9), pp. 1673-1689, (2007).        [ Links ]

David Elal-Olivero
Departamento de Matematicas
Facultad de Ingenieria
Universidad de Atacama
Copiapo
Chile
e-mail : delal@mat.uda.cl


Received : October 2009. Accepted : October 2010

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