An extension of the skew-generalized normal distribution and its derivation
DOI:
https://doi.org/10.4067/S0716-09172011000300007Keywords:
Asymmetry, Skew-Generalized Normal Distribution, Skew-Normal Distribution.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.
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[2] Azzalini, A. A class of distributions which includes the normal ones. Scandinavian Journal Statistics, 12, pp. 171—178, (1985).
[3] Azzalini, A. The skew-normal distribution and related multivariate families (with discussion). Scandinavian Journal Statistics, 32, pp. 159—188, (2005).
[4] Chiogna, M. Some results on the scalar skew-normal distribution. J. Ital. Statist. Soc., 7, pp. 1—13, (1998).
[5] Genton, M. G., Ed. Skew-elliptical distributions and their applications: a journey beyond normality. Chapman & Hall/CRC, (2004).
[6] Gómez, H. W., Venegas, O. and Bolfarine H. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics, 18, pp. 395—407, (2007).
[7] Gupta, A. K., Chang, F. C. and Huang, W. J. Some skew-symmetric model. Randon Operators Stochastic Equations, 10, pp. 133—140, (2002).
[8] Henze, N. A probabilistic representation of the skew-normal distribution. Scandinavian Journal Statistics, 13, pp. 271—275, (1986).
[9] Martinez, E., Varela, H., G´omez, 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).
[11] Pewsey, A. Problems of inference for Azzalini’s skew-normal distribution. Journal of Applied Statistics, 27(7), pp. 859—870, (2000).
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