Model selection with application to gamma process and inverse Gaussian process

Abstract

The gamma process and the inverse Gaussian process are widely used in condition-based maintenance. Both are suitable for modelling monotonically increasing degradation processes. Hence, one challenge for practitioners is determining which of the two processes is most appropriate in light of a real data set. 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.We conduct extensive numerical study to demonstrate the efficiency (in terms of sample size) of the proposed test statistic. We also indicate the conditions under which a gamma process can be well approximated by an inverse Gaussian process or the other way around.