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.

中文翻译：

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Burr III发行版的有用扩展

对于任何连续的基线G分布，Zografos和Balakrishnan（Statistical Methodology 6：344-362，2009）引入了由伽马生成的带有附加形状参数的分布族。基于这个族，我们定义了Burr III分布的新的四参数扩展。它可以具有递减，单峰和递减-递减-递减的风险率函数。我们提供了一些其结构特性的综合说明。我们提出了一个新的对数伽马Burr III回归模型，该模型可用于对四种现有的故障率类型进行建模。实际数据集的两个应用程序和仿真研究说明了新模型的性能。