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Volume 8
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Article

On Properties of the Bimodal Skew-Normal Distribution and an Application

by
David Elal-Olivero
1,
Juan F. Olivares-Pacheco
1,
Osvaldo Venegas
2,*,
Heleno Bolfarine
3 and
Héctor W. Gómez
4
1
Departamento de Matemáticas, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
2
Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
3
Instituto de Matemática e Estatística (IME), Universidade de São Paulo, São Paulo 05508-090, Brazil
4
Departamento de Matemática, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(5), 703; https://doi.org/10.3390/math8050703
Submission received: 10 March 2020 / Revised: 28 April 2020 / Accepted: 29 April 2020 / Published: 2 May 2020
(This article belongs to the Section D1: Probability and Statistics)
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Abstract

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.
Keywords: bimodal; simulation; skew-normal distribution; stochastic representation bimodal; simulation; skew-normal distribution; stochastic representation

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MDPI and ACS Style

Elal-Olivero, D.; Olivares-Pacheco, J.F.; Venegas, O.; Bolfarine, H.; Gómez, H.W. On Properties of the Bimodal Skew-Normal Distribution and an Application. Mathematics 2020, 8, 703. https://doi.org/10.3390/math8050703

AMA Style

Elal-Olivero D, Olivares-Pacheco JF, Venegas O, Bolfarine H, Gómez HW. On Properties of the Bimodal Skew-Normal Distribution and an Application. Mathematics. 2020; 8(5):703. https://doi.org/10.3390/math8050703

Chicago/Turabian Style

Elal-Olivero, David, Juan F. Olivares-Pacheco, Osvaldo Venegas, Heleno Bolfarine, and Héctor W. Gómez. 2020. "On Properties of the Bimodal Skew-Normal Distribution and an Application" Mathematics 8, no. 5: 703. https://doi.org/10.3390/math8050703

APA Style

Elal-Olivero, D., Olivares-Pacheco, J. F., Venegas, O., Bolfarine, H., & Gómez, H. W. (2020). On Properties of the Bimodal Skew-Normal Distribution and an Application. Mathematics, 8(5), 703. https://doi.org/10.3390/math8050703

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