A generalization of the Balakrishnan skew-normal distribution.

*(English)*Zbl 1237.62020Summary: 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.

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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\textit{I. Yadegari} et al., Stat. Probab. Lett. 78, No. 10, 1165--1167 (2008; Zbl 1237.62020)

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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 reportingâ€ť, 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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