The four-parameter Burr XII distribution: Properties, regression model, and applications

This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data.