A new modification of the Weibull distribution with mathematical characteristics: Its practical evidence from the radiation and energy system

In this paper, we introduce a new family of distributions, termed the New Flexible Lomax-X (NFLx-X) family, which incorporates two additional parameters to enhance the modelling flexibility of existing probability distributions. A four-parameter sub-model of the newly introduced method, called the New Flexible Lomax Weibull (NFLx-Weibull) distribution, is derived. Several statistical characteristics of the NFLx-Weibull model, including moments, the probability-weighted moments, stress-strength model, and entropy, are explored. The significance of the proposed distribution lies in its versatility, as it can exhibit left-skewed, right-skewed, and symmetrical density functions, as well as various failure rate behaviours, including decreasing, increasing, bathtub, and unimodal patterns. Additionally, for the NFLx-X family, we also investigate the general form of the moments, the moment-generating function, the quantile function, residual and reverse residual life, and order statistics. To estimate the model parameters of the proposed family of distributions, the Maximum Likelihood Estimation (MLE) method is employed. Similarly, a Monte Carlo simulation study is conducted to examine the performance of the proposed estimators under various sample sizes and parameter settings. Finally, the practical applicability and modelling flexibility of the proposed NFLx-Weibull distribution are demonstrated through a comparative analysis based on four real-world datasets from the radiation and energy systems sector.