A New Alpha Skew Normal Distribution and its Real Life Applications

Abstract

This paper introduces a novel continuous probability distribution which extends the alpha skew normal distribution of Elal-Olivero (2010). The newy introduced distribution is designed to model data exhibiting tri-modal behavior. A comprehensive overview of the novel distribution is provided including various key statistical properties like moments, moment generating function (mgf), characterization results etc. Besides, to assess the performance of the derived parameters, a simulation study is conducted using Metropolis- Hastings method. Furthermore, an investigation regarding the flexibility and applicability of the distribution is conducted by analyzing two real life datasets. During applications it is found that for the datasets considered, the newly proposed distribution outperforms the existing models in terms of some model selection criterion like AIC and BIC, highlighting its potential in practical applications. Finally, likelihood ratio (LR) test is conducted to differentiate between various nested models