On a New Class of Power-Transformed Bimodal Exponential Distributions with Inferential Procedures and Applications

Abstract

In this paper, we introduce a new three-parameter lifetime distribution that is obtained via a power transformation of the modified bimodal exponential model. The inclusion of an additional shape parameter significantly enhances the flexibility of the baseline distribution, allowing it to capture a wide range of distributional characteristics, including skewness, heavy tails, and varying hazard rate shapes such as increasing, decreasing, and non-monotonic forms. Several important structural properties of the proposed model are derived, including explicit expressions for the probability density function, cumulative distribution function, moments, and moment generating function. Entropy measures such as Rényi entropy, Shannon entropy, and cumulative residual entropy are also obtained. Key reliability characteristics, including the survival function, hazard rate function, cumulative hazard function, reversed hazard rate, and mean residual life function, are investigated in detail. A theoretical result on the modality of the distribution is established, demonstrating its ability to exhibit both unimodal and bimodal shapes. Parameter estimation is carried out using maximum likelihood estimation along with several alternative methods. A comprehensive simulation study is conducted to evaluate the performance of the estimators under different parameter settings. Finally, the applicability and effectiveness of the proposed distribution are demonstrated through the analysis of real datasets from reliability and environmental studies. Comparative results based on goodness-of-fit measures indicate that the proposed model provides a superior fit compared to several existing competing distributions.