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On Some Properties of the Beta Normal Distribution
Authors:Leandro C. Rêgo  Gauss M. Cordeiro
Affiliation:Departamento de Estatística , Universidade Federal de Pernambuco , Recife , PE , Brazil
Abstract:The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation for some properties and an analytical study of its bimodality. The hazard rate function and the limiting behavior are examined. We derive explicit expressions for moments, generating function, mean deviations using a power series expansion for the quantile function, and Shannon entropy.
Keywords:Beta normal distribution  Bimodality  Generating function  Hazard function  Mean deviation  Quantile function  Shannon entropy
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