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

TL;DR

This paper introduces a novel CUSUM sequential test with observation-adjusted control limits designed for rapid and adaptive detection of distribution changes in sequences with extremely heavy-tailed distributions, supported by theoretical analysis and simulations.

Contribution

It proposes a new CUSUM test with observation-adjusted control limits specifically for heavy-tailed distributions, providing theoretical ARL estimates and demonstrating effectiveness through simulations.

Findings

Accurate estimation of in-control and out-of-control ARLs for the proposed test.

Effective detection of alpha shifts in heavy-tailed distribution sequences.

Numerical simulations confirm the test's rapid detection capabilities.

Abstract

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.