Unit Extended Exponential Distribution with an Application to Engineering Datasets

In this paper, a novel probability distribution known as the unit extended exponential distribution is introduced, with the extended exponential distribution being put forth as the distribution of reference. It is important to note that the foundational distribution is defined by a set of two parameters, and the newly proposed distribution mirrors this characteristic by also being described by a pair of parameters. An extensive examination of various statistical characteristics of the recently introduced distribution is conducted, encompassing properties such as moments, skewness and kurtosis coefficients, stochastic ordering, among others. Furthermore, the investigation delves into the evaluation of the estimation technique through the utilization of the maximum likelihood function, which aids in the inference of the unknown parameters inherent in the newly formulated model. The effectiveness of these estimators is gauged considering factors such as bias and mean square error, leading to the identification of a significant discovery, followed by a detailed analysis of its functional behavior in relation to the sample size by means of employing Monte Carlo simulation. The emerging distribution appears to demonstrate superior efficacy and suitability for specific datasets within the domain of engineering sciences, as evidenced by an examination of three distinct datasets, complemented by a comparative analysis utilizing appropriate matching criteria when juxtaposed against alternative distributions.