Bimodality based on the generalized skew-normal distribution

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Authors
Venegas, Osvaldo
Salinas, Hugo S.
Gallardo, Diego I.
Bolfarine, Heleno
Gómez, Héctor W.
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Date
Datos de publicación:
Journal of Statistical Computation and Simulation, Vol.88, N° 1, 156-181, 2018
Keywords
Asimetría - Curtosis - Estimación de máxima verosimilitud - Distribución sesgada normal
Abstract
This paper focuses on the development of a new extension of the generalized skew-normal distribution introduced in Gomez et al. [Generalized skew-normal models: properties and inference. Statistics. 2006;40(6):495-505]. To produce the generalization a new parameter is introduced, the signal of which has the flexibility of yielding unimodal as well as bimodal distributions. We study its properties, derive a stochastic representation and state some expressions that facilitate moments derivation. Maximum likelihood is implemented via the EM algorithm which is based on the stochastic representation derived. We show that the Fisher information matrix is singular and discuss ways of getting round this problem. An illustration using real data reveals that the model can capture well special data features such as bimodality and asymmetry
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