Classical and Bayesian inference for the new four-parameter Lomax distribution with applications

In this study, a new four-parameter Lomax distribution is proposed using a new alpha power transformation technique. The new distribution is named "New Alpha Power Transformed Power Lomax Distribution." Mathematical properties, including moments, the moment-generating function, the mean residual life, order statistics, and the quantile function, are obtained. The maximum likelihood estimation approach is used to estimate the model parameters. A comprehensive simulation is used to evaluate the behavior of maximum likelihood estimators. Two real-world data sets were used to demonstrate the significance of the proposed model, and the results show that the new model performs better when interpreting lifetime data sets. In the end, for the data sets, Bayesian estimation and Metropolis-Hasting's approach were also utilized to construct the approximate Bayes estimates, and convergence diagnostic methods based on Markov Chain Monte Carlo techniques were applied.