A New Generalized Form of the Exponential Distribution: Properties and Application

In this article, we propose a new extension of the exponential distribution. We investigate some of their statistical properties, including moments, quantile and moment generating functions, emphasizing their utility in modeling diverse aging and failure criteria. One key advantage of the proposed distribution lies in its capacity to represent its density as a mixture of exponential densities, offering both symmetric and asymmetric shapes for greater modeling flexibility. The estimation of the model parameters is achieved through maximum likelihood estimation. The study presents comprehensive simulation results to assess the effectiveness of the proposed estimation technique. Furthermore, a practical application on real-world data is conducted to showcase the adaptability and versatility of the introduced distribution when compared with other extensions of the exponential model.Recently, many generalized families of distributions have been proposed and extensively used in modeling data in various applied sciences such as economics, finance, insurance, engineering and life testing. However, there is a clear need for extended forms of these distributions by adding one or more shape parameter(s) in order to obtain greater flexibility in modelling these data.