A useful extension of the Burr III distribution

For any continuous baseline G distribution, Zografos and Balakrishnan (Statistical Methodology 6:344–362, 2009) introduced the gamma-generated family of distributions with an extra shape parameter. Based on this family, we define a new four-parameter extension of the Burr III distribution. It can have decreasing, unimodal and decreasing-increasing-decreasing hazard rate function. We provide a comprehensive account of some of its structural properties. We propose a new log-gamma Burr III regression model, which is a feasible alternative for modeling the four existing types of failure rates. Two applications to real data sets and a simulation study illustrate the performance of the new models.