Statistics Seminars: The doubly geometric process and its properties
8 May 2017 15:15 in CM221
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 talk, 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.
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