On computing multiple change points for the gamma distribution

Abstract

This study proposes an efficient approach to detect one or more change points for gamma distribution. We plug a closed-form estimator into the gamma log-likelihood function to obtain a sharp approximation to the maximum of log-likelihood. We further derive a closed form calibration of approximate likelihood which is asymptotically equivalent to the exact log-likelihood. This circumvents iterative optimization procedures to find maximum likelihood estimates which can be a burden in detecting multiple change points. The simulation study shows that the approximation is accurate and the change points can be detected much faster. Two case studies on the time between events arising from industrial accidents are presented and extensively investigated.

Keywords:

• approximate likelihood
• calibration
• change point analysis
• industrial accidents
• likelihood ratio test
• time between events

Additional information

Funding

Ye was supported by the Natural Science Foundation of Jiangsu Province under grant BK20180232.

Notes on contributors

Xun Xiao

Dr. Xiao received the B.S. degree in Statistics from University of Science and Technology of China in 2011 and the PhD degree in systems engineering and engineering management from City University of Hong Kong. He is currently a Lecture in Statistics with School of Fundamental Sciences, Massey University, New Zealand. His research interests include reliability and quality control, industrial statistics, and spatial temporal modeling.

Piao Chen

Dr. Chen received the B.E. degree in industrial engineering from Shanghai Jiao Tong University, China, in 2013, and the Ph.D. degree in industrial systems engineering and management from the National University of Singapore in 2017. He is currently an Assistant Professor with Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands. His research interests include data analysis, reliability engineering and statistical inference.

Zhisheng Ye

Dr. Ye received the joint B.E. degree in material science and engineering and economics from Tsinghua University, Beijing, China in 2008, and the Ph.D. degree in industrial and systems engineering from the National University of Singapore in 2012. He is currently an Assistant Professor with the Department of Industrial Systems Engineering and Management, National University of Singapore. His research interests include reliability engineering, complex systems modeling, and industrial statistics.

Kwok-Leung Tsui

Dr. Tsui is the Chair Professor of Industrial Engineering in the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong. He is a Fellow of ASQ. His research interests include Quality Engineering, Process Control and Surveillance, System Informatics, Data Mining, Health Informatics, Bioinformatics, Infectious Disease Modeling, Logistics and Supply Chain Management.