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Some new results on the beta skew-normal distribution. (English) Zbl 1364.62036
Alleva, Giorgio (ed.) et al., Topics in theoretical and applied statistics. Selected papers based on the presentations at the 46th international meeting of the Italian Statistical Society, SIS, Rome, Italy, June 20–22, 2012. Cham: Springer (ISBN 978-3-319-27272-6/hbk; 978-3-319-27274-0/ebook). Studies in Theoretical and Applied Statistics. Selected Papers of the Statistical Societies, 25-36 (2016).
Summary: In this paper we study the Beta skew-normal distribution introduced by the authors [Commun. Stat., Theory Methods 42, No. 12, 2229–2244 (2013; Zbl 1287.60022)]. Some new properties of this distribution are derived including formulae for moments in particular cases and bi-modality properties. Furthermore, we provide expansions for its distribution and density functions. Bounds for the moments and the variance of the Beta skew-normal are derived. Some of the results presented in this work can be extended to the entire family of the Beta-generated distribution introduced by M. C. Jones [Test 13, No. 1, 1–43 (2004; Zbl 1110.62012)].
For the entire collection see [Zbl 1345.62013].

MSC:
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
62G30 Order statistics; empirical distribution functions
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