广义Pareto分布变点检测似然比模型

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广义Pareto分布变点检测似然比模型胡尧^1,2, 谌业文³1 贵州大学数学与统计学院, 贵阳 550025;
2 贵州大学贵州省公共大数据重点实验室, 贵阳 550025;
3 中山大学数学学院, 广州 510000 A Likelihood Ratio Model for Change Point Detection of Generalized Pareto Distribution HU Yao^1,2, CHEN Yewen³1 School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China;
2 Guizhou Provincial Key Laboratory of Public Big Data, Guizhou University, Guiyang 550025, China;
3 School of Mathematics, Sun Yat-sen University, Guangzhou 510000, China

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摘要为检测极端事件的状态变化，基于似然比方法研究了广义Pareto分布（Generalized Pareto Distribution，GPD）变点检测模型.考虑三参数GPD变点的检验问题，提出了最大似然比检验统计量.通过证明参数变换后GPD的对数似然和检验统计量的一系列极限性质，得到了检验统计量的渐近分布.通过模拟研究，对该方法的有限样本性质进行了评价，实例分析也验证了该方法的可行性.

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收稿日期: 2019-01-06

PACS:

O212.1

基金资助:国家自然科学基金（11661018），贵州省科技计划项目（黔科合平台人才[2017]5788号），贵州省数据驱动建模学习与优化创新团队（黔科合平台人才[2020]5016号），全国统计科学研究（2014LZ46），贵州省自然科学基金（黔科合J字[2014]2058号）资助项目.

引用本文:

胡尧, 谌业文. 广义Pareto分布变点检测似然比模型[J]. 应用数学学报, 2021, 44(4): 553-573. HU Yao, CHEN Yewen. A Likelihood Ratio Model for Change Point Detection of Generalized Pareto Distribution. Acta Mathematicae Applicatae Sinica, 2021, 44(4): 553-573.

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