独立泊松序列与指数序列的变点检测方法比较

Comparison of Change Point Detection Methods for Independent Poisson Sequences and Exponential Sequences

变点检测问题是近年来数理统计研究领域的一个研究热点。文章基于R软件Changepoint程序包,借助模拟研究并应用三种常见的变点检测方法,分别对泊松和指数序列的均值方差变点进行检测。从不同的样本量、分布参数变化、变点个数、优化函数中使用不同惩罚项的角度,综合考察比较了三种方法对两类分布序列变点检测的效果。并针对英国矿难发生次数的经典实际数据实证,揭示了三种方法对该数据的变点检测效果,也验证了模拟结果的可靠性。

Change point detection has become a hot spot in the field of mathematical statistics research in recent years.Based on change point package of R software, this paper applies three common change point detection methods by means of simulation to respectively test the mean variance change point of poisson sequence and exponential sequence. And then from the perspective of using different penalty items in different sample size, distribution parameter changes, change point numbers and optimization function, the paper comprehensively investigates and compares the effect of three methods on the detection of two types of distribution sequences. Finally, according to the classic empirical data on the number of mining accidents in the UK, the paper, reveals the change point detection effect of the three methods on the data, and also verifies the reliability of the simulation results.