This article presents a novel statistical distribution, known as the DUS exponential distribution, and conducts a comprehensive examination of its essential characteristics and applications. In this study, the fundamental properties of the distribution such as reliability, survival and hazard function, stress-strength reliability, moments, order statistics, entropy function, moment generating function, as well as Bonferroni and Lorenz curves are studied. The estimation of parameters by the maximum likelihood estimation method is discussed. The article also explores the reliability of the upgraded system using three different approaches: reduction, hot duplication, and cold duplication methods. To validate the efficacy of maximum likelihood estimators, a comprehensive simulation study is conducted. Finally, the authors of this article have analyzed real-life data sets from banking sector and medical science, and it has been found that the proposed DUS exponential distribution provides a better fit compared to other distributions.
Qayoom et al. (Wed,) studied this question.
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