On the Type I Half Logistic Lomax Distribution with Applications

Abstract

In this research, a new four-parameter lifetime distribution called the Type I Half-Logistic exponentiated Lomax distribution is introduced. The study presents various mathematical properties of this novel model, including moments, moment generating function, quantile function, survival function, and hazard function. Additionally, the behavior of the probability density function for both the maximum and minimum order statistics is analyzed within the framework of this new distribution. The paper also explores parameter estimation using the maximum likelihood method to estimate the distribution's unknown parameters. To validate the practicality and versatility of the proposed distribution, three real-life datasets are used for empirical validation. Comparisons are made with existing lifetime distributions from the literature, and the results consistently demonstrate that the proposed distribution outperforms others in termsof fit and flexibility for all three datasets. This highlights its effectiveness in modeling diverse real-world scenarios. The introduction of the Type I Half-Logistic exponentiated Lomax distribution contributes to the expansion of distribution theory and offers a valuable tool for researchers, statisticians, and analysts to accurately model and analyze lifetime data in various fields. The analytical properties derived in this study provide a solid foundation for future research and applications, and the successful parameter estimation and goodness-of-fit results further validate the practical significance of the proposed distribution.