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

• Main Authors: David Elal-Olivero, Juan F. Olivares-Pacheco, Osvaldo Venegas, Heleno Bolfarine, Héctor W. Gómez
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Mathematics
• Subjects: bimodal; simulation; skew-normal distribution; stochastic representation
• Online Access: https://www.mdpi.com/2227-7390/8/5/703

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.