A Flexible Probability Model for Reliability Data Analysis: The Extended Half-Normal Distribution with Further Results

Abstract

Recent years have shown growth in the potential applications of extensions of skew and half-normal distributions. In this paper, we provide and study, in detail, an extended class of such distributions. The presented distribution has a scale parameter and two shape parameters. The motivations behind the development of this distribution are: 1- the probability distribution function has skewed, unimodal and bathtub shapes with different styles and the hazard rate function is increasing with various shapes, which makes this distribution flexible enough to analyze reliability data; 2- it can be expressed as a mixture of the Generalized Half-Normal distribution and the new weighted Generalized Half-Normal distribution. A number of statistical results are derived. Monte Carlo simulation analysis is carried out with Maximum Likelihood Estimation to assess the performance of this technique for a variety of the distribution parameter values. The power of the distribution is demonstrated with real applications using two reliability datasets from the industry. The results reveal that the proposed distribution outperformed the Generalized Lindley, Exponentiated Exponential, Gamma, Alpha-Skew-Normal, the Half-Alpha- Skew-Normal, and the Modified Generalized Half-Normal distributions.