A Generalization of the Skew-Normal Distribution: The Beta Skew-Normal |
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Authors: | Valentina Mameli Monica Musio |
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Institution: | 1. Dipartimento di Matematica , Università di Cagliari , Cagliari , Italy mameli.valentina@virgilio.it;3. Dipartimento di Matematica , Università di Cagliari , Cagliari , Italy |
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Abstract: | We consider a new generalization of the skew-normal distribution introduced by Azzalini (1985
Azzalini , A. ( 1985 ). A class of distributions which includes the normal ones . Scand. J. Statis. 12 ( 2 ): 171 – 178 .Web of Science ®] , Google Scholar]). We denote this distribution Beta skew-normal (BSN) since it is a special case of the Beta generated distribution (Jones, 2004
Jones , M. C. ( 2004 ). Families of distributions of order statistics . Test 13 ( 1 ): 1 – 43 .Crossref], Web of Science ®] , Google Scholar]). Some properties of the BSN are studied. We pay attention to some generalizations of the skew-normal distribution (Bahrami et al., 2009
Bahrami , W. ,
Agahi , H. ,
Rangin , H. ( 2009 ). A two-parameter Balakrishnan skew-normal distribution . J. Statist. Res. Iran 6 : 231 – 242 . Google Scholar]; Sharafi and Behboodian, 2008
Sharafi , M. ,
Behboodian , J. ( 2008 ). The Balakrishnan skew-normal density . Statist. Pap. 49 : 769 – 778 .Crossref], Web of Science ®] , Google Scholar]; Yadegari et al., 2008
Yadegari , I. ,
Gerami , A. ,
Khaledi , M. J. ( 2008 ). A generalization of the Balakrishnan skew-normal distribution . Statist. Probab. Lett. 78 : 1165 – 1167 .Crossref], Web of Science ®] , Google Scholar]) and to their relations with the BSN. |
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Keywords: | Balakrishnan skew-normal Beta skew-normal Order statistics Skew-normal distribution |
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