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A generalization of the Balakrishnan skew-normal distribution. (English) Zbl 1237.62020
Summary: The skew-normal distribution belongs to a family of distributions which includes the normal distribution along with an extra parameter to regulate skewness. A. Azzalini [Scand. J. Stat., Theory Appl. 12, 171–178 (1985; Zbl 0581.62014)] was the first to introduce the skew-normal distribution and studied some of its properties. N. Balakrishnan [Test 11, No. 1, 37–39 (2002)] in his discussion of the paper of B.C. Arnold and R.J. Beaver, Test 11, No. 1, 7–54 (2002; Zbl 1033.62013), later proposed a generalization of this distribution.
In this paper, we introduce a new generalization of the Balakrishnan skew-normal distribution by explaining some important properties of this distribution. Also, we have described three methods for constructing this distribution. Finally, its multivariate extension has been presented.

MSC:
62E10 Characterization and structure theory of statistical distributions
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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References:
[1] Arnold, B.C.; Beaver, R.J., Skewed multivariate models related to hidden truncation and/or selective reporting (with discussion), Test, II, 7-54, (2002) · Zbl 1033.62013
[2] Azzalini, A., A class of distributions which includes the normal ones, Scandinavian journal of statistics, 12, 171-178, (1985) · Zbl 0581.62014
[3] Azzalini, A.; Dalla Valle, A., The multivariate skew-normal distribution, Biometrika, 83, 715-726, (1996) · Zbl 0885.62062
[4] Balakrishnan, N., Discussion of “skewed multivariate models related to hidden truncation and/or selective reporting”, Test, 11, 37-39, (2002)
[5] Gupta, R.C.; Gupta, R.D., Generalized skew-normal model, Test, 13, 2, 501-524, (2004) · Zbl 1076.62096
[6] Sharafi, M, Behboodian, J., 2007. The Balakrishnan skew-normal density, Statistical Papers (in press) · Zbl 1309.60008
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