A self-normalization test for a change-point in the shape parameter of a gamma distributed sequence

In this paper, a parametric change-point problem encountered in analyzing a gamma distributed sequence is considered. We propose a self-normalization based CUSUM type test statistic to detect the presence of a change-point, and obtain its limiting null distribution. The CUSUM-based procedure for detecting the location of this change-point is also given. At the same time, simulation results are provided, which show that our procedures are effective.