The CUSUM Test with Observation-Adjusted Control Limits in Parameters Change Detection for the Extremely Heavy-Tailed Distributions Sequences

In this paper, we propose an new the CUSUM sequential test (control chart, stopping time) with the observation-adjusted control limits (CUSUM-OAL) for monitoring quickly and adaptively the change in distribution of a sequential observations. We give the estimation of the in-control and the out-of-control average run lengths (ARLs) of the CUSUM-OAL test. The theoretical results are illustrated by numerical simulations in detecting $\alpha$ shifts of the extreme heavy-tailed distribution observations sequence.