Model selection with application to gamma process and inverse Gaussian process

The gamma process and the inverse Gaussian process are widely used in condition-based maintenance. Both are suitable for modelling monotonically increasing degradation processes. One challenge for practitioners is determining which of the two processes is most appropriate in light of a real data set. A common practice is to select the one with a larger maximized likelihood. However, due to variations in the data, the maximized likelihood of the “wrong” model could be larger than that of the “right” model. This paper proposes an efficient and broadly applicable test statistic for model selection. The construction of the test statistic is based on the Fisher information. Extensive numerical study is conducted to indicate the conditions under which the gamma process can be well approximated by the inverse Gaussian process, or the other way around