Analysis of engineering data with an innovative generalization of the Lomax distribution.

Abstract

As the amount and complexity of engineering data that need to be analyzed and interpreted continue to increase, the development of new distributions with outstanding adaptability is necessary. The aim of this work is to improve the precision of data modeling, particularly with respect to reliability and lifetime analyses. In this regard, a novel distribution called the Lomax Kavya Manoharan exponential (LKME) distribution derived from the exponential form of a hazard rate function is proposed. The introduction of the Kavya Manoharan exponential distribution with the properties of the Lomax distribution promotes the adaptability to capture different patterns of failure rates, thereby providing a better fit for lifetime data. The LKME distribution is highly flexible and accommodates almost all possible forms of densities, including symmetric, skewed, and inverted J-shaped, as well as diverse shapes of the hazard rate function. This ensures its suitability for modeling various applications in engineering and other fields. Monte Carlo simulations are performed to examine the performance of several classical estimation methods according to benchmarks, such as absolute bias and mean squared error. Furthermore, five engineering datasets are analyzed using the novel LKME distribution, which provides a better fit than comparison distributions, as demonstrated by different goodness-of-fit metrics.