Several Properties and Estimation of a New Generalized Lomax Distribution with Applications to COVID-19 Data

Abstract

The main goal of this paper is to provide a new version of the Lomax distribution by introducing an additional shape parameter to enhance its adaptability. The modified alpha power transformed methodology is employed to develop the new version. Various structural properties of the new model are derived, comprising the quantile function, some moments, Lorenz and Bonferroni curves, entropies, order statistics, and stress-strength reliability. The parameters of the new version of the Lomax distribution are estimated utilizing the maximum likelihood estimation technique. A simulation analysis is performed to assess the effectiveness of the estimators obtained from the novel model, applying criteria such as mean squared error and bias. Three distinct applications related to COVID-19 and engineering data are employed to demonstrate the flexibility of the model.