The single and double inverse Pareto–Burr XII distribution: Properties, estimation methods, and real-life data applications

Researchers consistently improve statistical tools to provide a flexible method to fit or predict. The solution needs to be more suitable since the approach is sometimes complex and complicated. Generally, statistical tools are generated from ordinary least squares and wavelet methods. However, the reliability tool provides a good fit comparable to state-of-the-art methods, including the complex posterior setting of hyperparameters. In this article, a flexible extension of the Burr XII model, which is the odd inverse Pareto–Burr XII (OIPBXII) distribution, is studied and investigated using statistical tools such as Markov chain Monte Carlo methods. The mathematical properties of the probability density distribution of OIPBXII are derived, and it shows a behavior shape, decreasing, increasing, J-shaped, reversed-J-shaped, bathtub, upside-down bathtub, decreasing–increasing–decreasing hazard rates, and right-skewed, symmetrical, and concave down densities. The OIPBXII parameters are investigated by using seven classical approaches to estimation. Extensive simulation results are presented to explore the performance of these methods for small and large samples. An application to two real-life sets of data from engineering and medicine is analyzed, showing the flexibility of the OIPBXII distribution as compared to existing Burr XII distributions.