Bimodality based on generalized skew-normal distribution.

29 septiembre, 2017 -


Osvaldo Venegas(a), Hugo S. Salinas(b), Diego I. Gallardo(b), Heleno Bolfarine(c), Héctor W. Gómez(d).


(a) Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco, Chile.
(b) Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó, Chile.
(c) Departamento de Estadística, IME, Universidade de Sao Paulo, Sao Paulo, Brazil.
(d) Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile.


JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
Volumen: 88(1) Páginas: 156-181.
DOI: https://doi.org/10.1080/00949655.2017.1381698
Fecha de Publicación: 29 de Septiembre de 2017.


Abstract

This paper focuses on the development of a new extension of the generalized skew-normal distribution introduced in Gómez 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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