On computing multiple change points for the gamma distribution

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.

Automated summary

This study introduces an efficient approach to detect change points in gamma distribution by plugging an estimator into the gamma log-likelihood function to obtain an approximation. Through simulation and case studies, it is shown that this method is accurate and quick in detecting change points.