The Power Burr Type X Distribution: Properties, Regression Modeling and Applications

Abstract

In probability theory, researchers always prefer a model having simple structure with small estimation cost and higher adequacy for real life data applications. Therefore, in this study we have developed a simple power Burr X (PBX) distribution with an additional shape parameter. We have studied the shapes of the developed distribution with respect to subfamilies depends on the additional parameter. This study reveals some structural properties of this new model such as moments, stochastic ordering, quantile function and Rnyi entropy. We have also developed a location-scale regression model for log power Burr X (LPBX) distribution to enhance its application in survival analysis. To observe the behavior of estimated parameters, we have conducted a Monte Carlo simulation study under maximum likelihood (ML) estimation and observed efficiencies by means of bias and mean square errors. Three life-time applications from different industries justified the adequacy, flexibility and potentiality of PBX distribution as compared to other higher parametric complex generalizations.