On computing multiple change points for the gamma distribution

Journal article (2021)

Authors

Xun Xiao Massey University
Piao Chen Institute of High Performance Computing
Zhisheng Ye National University of Singapore
Kwok Leung Tsui City University of Hong Kong
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Published Date

2021

Language

English

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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.