An extension of the generalized half-normal distribution
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In this paper we propose an extension of the generalized half-normal distribution studied in Cooray and Ananda (Commun Stat 37:1323–1337, 2008). This new distribution is defined by considering the quotient of two random variables, the one in the numerator being a generalized half normal distribution and the one in the denominator being a power of the uniform distribution on \((0,1)\), respectively. The resulting distribution has greater kurtosis than the generalized half normal distribution. The density function of this more general distribution is derived jointly with some of its properties and moments. We discuss stochastic representation, maximum likelihood and moments estimation. Applications to real data sets are reported revealing that the proposed distribution can fit real data better than the slashed half-normal, generalized half-normal and Birnbaum–Saunders distributions.
KeywordsGeneralized half-normal distribution Slash distribution Slashed half-normal Kurtosis
The authors acknowledge helpful comments and suggestions by two referees which substantially improved the presentation. The research of N. M. Olmos was supported by Beca Tesis de Postgrado de la Dirección de la Escuela de Postgrado de la Universidad de Antofagasta (Chile). The research of H. Bolfarine was supported by CNPq (Brazil). The research of H. W. Gómez was supported by FONDECYT (Chile) \(1090411\).
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