A Bimodal Extension of the Tanh Skew Normal Distribution: Properties and Applications

This article introduces a novel family of skew distributions namely bimodal Tanh skew normal (BTSN) distributions, which incorporates a new skew function with the help of hyperbolic tangent function. This new distribution is designed to accommodate data sets with two modes. Besides, the article presents various essential mathematical properties, such as moments, moment generating function, characteristic function, mean deviation, characterizations and the method for maximum likelihood estimation of this distribution. A simulation study is also conducted using Metropolis-Hastings algorithm to examine the behavior of the obtained parameters. Furthermore, the practical utility of this new distribution is demonstrated through a real life application involving a specific data set. To assess the suitability of the BTSN distribution, the article employs Akaike information criterion (AIC) and Bayesian information criterion (BIC). Finally, a likelihood ratio test is conducted to distinguish between the new model and the existing competing models.