Properties and Application of Trimodal Skew Normal Distribution

Abstract

A new type of continuous distribution that extends the skew distribution developed by Azzalini (1985) is presented in this paper. This new distribution is designed to effectively model real-life data that may have up to three modes. The primary objective of this study is to provide a comprehensive understanding of the structural properties of this distribution, including moments, moments generating function, Fisher's information matrix, characterization, and parameter estimation through the method of maximum likelihood. Additionally, the distribution's flexibility and usefulness are evaluated by analyzing two real-life datasets. The analysis findings suggest that, as measured by AIC and BIC values, the new distribution demonstrates superior performance in fitting the datasets compared to other distributions. The lower values of AIC and BIC suggest that the new distribution better fits the datasets compared to other alternatives.