A New Generalization of Lomax Distribution: Estimation and Modelling for Medical Data

In this study, a new three-parameter Lomax distribution is proposed using the beta transformation technique. The new distribution is named Beta Transformed Lomax distribution. Some mathematical properties of the proposed distribution were derived, including moments, the moment-generating function, the mean residual life, quantile function, reliability function, failure rate, and order statistics. The model parameters were estimated using the maximum likelihood approach. The performance of the estimation method was evaluated using a simulation study. Two medical data sets were analyzed using a new distribution and the modeling performance was compared with other generalizations of Lomax distributions, and the results show that the new model performs better than others. Also, the Metropolis-Hastings approach within Bayesian estimation was used to obtain approximate Bayes estimates, and convergence diagnostics based on Markov Chain Monte Carlo techniques were conducted.