广义泊松计数模型及其统计推断  

The Generalized Poisson Count Technique and its Statistical Inference

作　　者：吴琴[1] 刘寅[2] 阮建 WU Qin;LIU Yin;RUAN Jian(School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China;School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China;Zhongshan Haotou Middle School,Zhongshan 528437,China)

机构地区：[1]华南师范大学数学科学学院,广州510631 [2]中南财经政法大学统计与数学学院,武汉430073 [3]中山市濠头中学,中山528437

出　　处：《华南师范大学学报（自然科学版）》2019年第6期107-110,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11401226,11601524);广东省自然科学基金项目(2017A030310264)

摘　　要：基于广义泊松分布的性质,提出了广义泊松计数模型,解决了泊松计数模型中对照组数据过度分散和过度集中的问题.在模型的统计推断中,通过引入缺失数据和构建替代函数,研究了使用EM算法、MM算法计算模型中参数极大似然估计的迭代收敛算法.进一步地,通过统计模拟展示迭代算法中参数估计的误差,对模拟结果进行讨论得到有效的信息.Based on the Generalized Poisson distribution,the Generalized Poisson Count Technique is introduced to solve the over-dispersion and under-dispersion in the Poisson Item Count Technique.For the statistical inference,the iterative algorithm using EM algorithm and MM algorithm is studied to calculate the maximum likelihood estimate in the model by introducing the missing data and constructing the substitution function.Furthermore,in the simulation,the bias of the estimate is presented and the simulation results are discussed to find effective information.

关 键 词：广义泊松分布 EM算法 MM算法 参数估计 模拟 

分 类 号：O212.6[理学—概率论与数理统计]