Bimodality based on the generalized skew-normal distribution

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.

KEYWORDS:

• Asymmetry
• bimodality
• kurtosis
• maximum likelihood estimation
• skew-symmetric distributions

Acknowledgements

We acknowledge two referees for comments and suggestions that substantially improved the presentation.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of H. W. Gómez was supported by SEMILLERO UA-2017 (Chile). The research of H. Bolfarine was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Brazil.