Statistical Inference and Mathematical Properties of Burr X Logistic-Exponential Distribution with Applications to Engineering Data

The Burr X logistic-exponential distribution is introduced in this study as a novel logistic-exponential distribution extension that may be utilized to efficiently describe engineering data. There are J-shape, symmetrical, left-skewed, reversed-J shape, and right-skewed densities available, as well as decreasing, rising, bathtub, unimodal, J-shape, and reversed-J shape hazard rates. The fundamental mathematical features of the proposed model were obtained. The new model’s parameters were estimated using seven different approaches, including maximum likelihood, Anderson–Darling, maximum product of spacing, least-squares, Cramér–von Mises, percentiles, and weighted least squares. To evaluate the performance of the recommended estimation methods, a full simulation study was carried out. Finally, the adaptability of the provided distribution was tested using two real datasets from engineering science, revealing that the new model can yield a close match when compared to competing models.