复合Rayleigh分布均值变点估计的相合性  

THE CONGRUENCE THE ETIMATOR FOR THE CHANGEPOINT OF COMPOUND RAYLEIGH DISTRIBUTION

作　　者：李湘艺 周菊玲[1] Li Xiangyi;Zhou Juling(School of Mathematical Science,Xinjiang Normal University,830017,Urumqi,China)

机构地区：[1]新疆师范大学数学科学学院,乌鲁木齐830017

出　　处：《山东师范大学学报（自然科学版）》2023年第1期16-21,共6页Journal of Shandong Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11801488);新疆师范大学教学研究与改革资助项目(SDJG2020-30);新疆师范大学科研发展专项资助项目(XJNUZX202001)。

摘　　要：变点问题是数理统计、应用数学、信息科学中非常重要的一类问题.随着统计方法的不断完善,对于变点问题的研究也有了更深一步的发展.本文利用CUSUM方法,研究了复合Rayleigh分布尺度参数的均值变点估计问题.首先,在样本为等距离时刻观测而出的条件下,定义了变点的检验统计量;其次,检验变点的存在;最后,在方差不变的情况下,证明了均值变点估计的相合性,并且得到了其收敛速度.Change point problem is a very important problem in mathematical statistics,applied mathematics and information science.And the research on the change point problem has been further developed with the continuous improvement of statistical methods.In this paper,the mean change point estimation of composite Rayleigh distribution scale parameter is studied by using CUSUM methods.First,the test statistic of change point is defined under the condition that the sample is observed at constant distance.Secondly,check the existence of change point.Finally,the consistency of the estimation of mean change point is proved under the condition of constant variance,and the convergence rate is obtained.

关 键 词：复合Rayleigh分布 变点 CUSUM方法 相合性 收敛速度 

分 类 号：O212[理学—概率论与数理统计]