广义指数分布参数变点的检验

Detecting Parameters Change Points in the Generalized Exponential Distribution

摘要: 本文分别提出了检验广义指数分布位置参数及尺度参数变点的似然比方法和CUSUM方法，并针对尺度参数无显式估计导致检验统计量的临界值不易计算的问题，提出了用于近似统计量临界值的Bootstrap方法。模拟结果表明，似然比方法在检验位置参数变点时优于CUSUM方法，但无法检验出尺度参数变点，而CUSUM方法对两类参数变点都有较好的检验效果，结合两种方法能区分出两类参数变点。最后应用本文方法分析了一组电压数据，说明所给方法的有效性和实用性。

Abstract: This paper proposes a likelihood ratio method and a CUSUM method to detect change points of lo-cation parameters and scale parameters in the generalized exponential distribution. A Bootstrap method is introduced to approximate the critical values of the statistics for the scale parameters change points without explicit estimation leading to the critical values of statistic not easy to cal-culate. Simulations show that the likelihood ratio method is better than the CUSUM method when detecting change points of location parameters, however, the likelihood ratio statistic can’t test change points of scale parameters. While the CUSUM method has the good performance testing two kinds of parameters change points. Combining the two methods can differentiate location pa-rameters and scale parameters change points. Finally, the validity of proposed methods is demon-strated by analyzing a set of voltage data.