Abstract
In this paper we study the Beta skew-normal distribution introduced by Mameli and Musio (2013). 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 Jones (Test 13(1):1–43, 2004).
Keywords
- Skew-normal Distribution (SN)
- Bi-modality Properties
- Generalized Beta Distribution
- Mameli
- Exact Closed-form Expressions
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The authors acknowledge helpful suggestions from the editors and an anonymous referee.
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Mameli, V., Musio, M. (2016). Some New Results on the Beta Skew-Normal Distribution. In: Alleva, G., Giommi, A. (eds) Topics in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Cham. https://doi.org/10.1007/978-3-319-27274-0_3
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DOI: https://doi.org/10.1007/978-3-319-27274-0_3
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