Doubly geometric processes and applications
针对传统几何过程只能模拟单调变化和固定形状参数的局限，提出双重几何过程，推导概率性质并给出两种参数估计方法，在保修索赔数据拟合中表现优于其他常用模型。
The geometric process has attracted extensive research attention from authors in reliability mathematics since its introduction. However, it possesses some limitations, which include that: (1) it can merely model stochastically increasing or decreasing inter-arrival times of recurrent event processes and (2) it cannot model recurrent event processes where the inter-arrival time distributions have varying shape parameters. Those limitations may prevent it from a wider application in the real world. In this paper, we extend the geometric process to a new process, the doubly geometric process, which overcomes the above two limitations. Probability properties are derived, and two methods of parameter estimation are given. Application of the proposed model is presented: one is on fitting warranty claim data, and the other is to compare the performance of the doubly geometric process with the performance of other widely used models in fitting real-world datasets, based on the corrected Akaike information criterion.