The Multimodal Extension of the Balakrishnan Alpha Skew Normal Distribution: Properties and Applications

Abstract

This paper introduces a new class of Balakrishnan distribution by extending the multimodal skew-normal distribution proposed by Chakraborty et al. (2015). Statistical properties of the new family of distributions are studied in detail. In particular, explicit expressions of the density and distribution function, moments, skewness, kurtosis and the moments generating function are derived. Furthermore, estimation of the parameters using the maximum likelihood method of the new family of distributions is considered. Finally, the paper ends with an illustration of real-life data sets and then comparing the value of Akaike Information Criterion and Bayesian information criterion of the new distribution with some other known distributions. For the nested models, the Likelihood Ratio Test is carried out.

Multimodal Alpha Skew Normal Distribution: A New Distribution to Model Skewed Multimodal Observations

“…are the pdf and cdf of standard normal distribution respectively. A lot of extensions and generalizations of this distribution were proposed and studied (for details see Hazarika, 2011, Ali et al (2008), Arnold and Beaver (2000), Shah et al (2022), Shah et al (2023a), Shah et al (2023b) and among others). We focus on two extensions namely the alpha skew normal () ASN distribution of Elal-Olivero (2010) and the multimodal skew normal (MMSN) distribution of Chakraborty et al (2015).…”

Balakrishnan Alpha Skew Generalized t Distribution: Properties and Applications

“…Recently, skewed distribution played a very prominent role in statistical literature to overcome the difficulty to handle real-life skewed data sets. Using the novel idea of (2) , many researchers exclusively studied the non-normal asymmetric distributions; see for example (3)(4)(5)(6)(7)(8) .…”