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.

摘要

这项研究提出了一种有效的方法来检测伽马分布的一个或多个变化点。我们将一个封闭形式的估计器插入到伽马对数似然函数中，以获得对数似然最大值的急剧近似。我们进一步推导出近似似然的封闭形式校准，其渐近等效于精确对数似然。这绕过了寻找最大似然估计的迭代优化程序，这可能是检测多个变化点的负担。仿真研究表明近似是准确的，并且可以更快地检测到变化点。介绍了两个关于工业事故事件间隔时间的案例研究，并进行了广泛的调查。