A Novel Extended Power-Lomax Distribution for Modeling Real-Life Data: Properties and Inference

One of the important features of generalized distribution is its ability and flexibility to model real-life data in several applied fields such as medicine, engineering, and survival analysis, among others. In this paper, a flexible four-parameter Lomax extension called the alpha-power power-Lomax (APPLx) distribution is introduced. The APPLx distribution is analytically tractable, and it can be used quite effectively for real-life data analysis. Key mathematical properties of the APPLx distribution including mode, moments, stress-strength reliability, quantile and generating functions, and order statistics are presented. The APPEx parameters are estimated by using eight classical estimation methods. Extensive simulation studies are provided to explore the performance of the proposed estimation methods and to provide a guideline for practitioners and engineers to choose the best estimation method. Three real-life datasets from applied fields are fitted to assess empirically the flexibility of the APPLx distribution. The APPLx distribution shows greater flexibility as compared to the McDonal–Lomax, Fréchet Topp–Leone Lomax, transmuted Weibull–Lomax, Kumaraswamy–Lomax, beta exponentiated-Lomax, Weibull–Lomax, Burr-X Lomax, Lomax–Weibull, odd exponentiated half-logistic Lomax, and alpha-power Lomax distributions