The Weimal distribution: Its properties and applications

Abstract

The normal distribution is one of the most popular probability distributions with applications to real life data. In this paper, an extension of this distribution called the Weimal distribution which is believed to provide greater flexibility to model scenarios involving skewed datawas proposed. The probability density function of the new distribution can be represented as a linear combination of exponentiated normal density functions. Analytical expressions for some mathematical quantities comprising moments, moment generating function, characteristics function and order statistics werepresented. The estimation of the proposed distribution’s parameters was undertaken using the method of maximum likelihood estimation. For illustration and performance evaluation of the proposed model, two real-life datasets adapted from earlier studies were used. The results of the comparative analysis to other baseline models showed that the proposed distribution would be more appropriate when dealing with skewed data.