Sequential change-point detection for skew normal distribution

Abstract

In this article, we propose a modified max-cumulative sum (CUSUM) procedure for detecting changes in parameters of skew normal distribution. The corresponding false alarms frequency and the postchange detection delay are investigated. Asymptotic behaviors of detection delay and theoretical optimality of the detection procedure have been established. Simulations have been conducted to show the performance of the proposed method and compare it to the other existing methods including CUSUM. Real data are given to illustrate the detection procedure.

KEYWORDS:

• Change point detection
• CUSUM
• sequential test
• skew normal distribution

SUBJECT CLASSIFICATIONS:

• 62F03
• 62L10
• 62L15

ACKNOWLEDGMENTS

The authors are grateful to the Editor-in-Chief, Dr. Nitis Mukhopadhyay, and two anonymous reviewers for their helpful comments on improving the contents of this article.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

This work was supported by the Simons Fundation.