Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution.

We develop a new continuous distribution called the beta-Burr type X distribution that extends the Burr type X distribution. The properties provide a comprehensive mathematical treatment of this distribution. Further more, various structural properties of the new distribution are derived, that includes moment generating function and the rth moment thus generalizing some results in the literature. We also obtain expressions for the density, moment generating function and rth moment of the order statistics. We consider the maximum likelihood estimation to estimate the parameters. Additionally, the asymptotic confidence intervals for the parameters are derived from the Fisher information matrix. Finally, simulation study is carried at under varying sample size to assess the performance of this model. Illustration the real dataset indicates that this new distribution can serve as a good alternative model to model positive real data in many areas.

In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.

This study introduces and applies a novel statistical model known as the hybrid Weibull inverse Weibull (HWIW) distribution, which combines the characteristics of the Weibull and inverse Weibull distributions to provide a more flexible model for representing real-world data, especially those characterized by asymmetry or extreme values. The basic functions of the distribution were derived, along with other statistical measures such as moments, the quantile function, and entropy were also derived. The distribution parameters were estimated using three distinct approaches, and their performance was evaluated through a Monte Carlo simulation to assess the performance and precision of each estimation technique. The results were used to show the most accurate estimation method for different samples. The proposed model was utilized to test two practical datasets; the findings demonstrated that the HWIW distribution outperformed six competing IW distributions in terms of model selection metrics. These results confirm the efficiency of the HWIW model’s ability to capture the structure of complex datasets and open the way for its use in multiple applications, including medical, industrial, and social fields, with the potential to be expanded to include multidimensional data or integrated with artificial intelligence techniques.