基于Gamma分布缺失数据的分位数估计
发布时间：2018-07-20 12:58
【摘要】：缺失数据普遍存在于实验研究和社会调查领域中,数据缺失问题造成分析任务加重和统计结果的不准确性.如何有效的处理缺失数据,怎样才能充分利用数据信息,准确地反映研究群体的特征,达到预期研究目的,已成为当前统计研究中的难点和热点问题.由于缺失数据往往包含了总体的一些重要信息,要想把统计分析的方法应用到处理缺失数据的领域,大体思路就是先对不完备数据进行填补,从而得到完整的数据集,再对这个数据集进行分析,所得到的结论才能保证准确的反应真实情况.本文针对非随机缺失机制下的数据缺失问题,在一定的假设前提下,由已观察数据,利用概率统计的方法给出补充数据,并结合矩估计给出了分布参数的统计推断,进而给出完全数据的概率分布的分位数估计,我们比较关心的是中位数(0.5分位数)、四分位数(分别是第一四分位数/0.25-分位数,第三四分位数/0.75-分位数)以及0.05分位数和0.95分位数.同时我们在总体服从Gamma分布,并且成功概率为指数分布(参数λ可根据Gamma分布的参数和缺失数据比例来给定)的假设下,对Gamma分布的参数和分位数做了估计,给出了参数的迭代公式.在模拟研究阶段,利用R语言,分别对缺失比例为1/10、1/5、1/2、2/3进行了模拟研究,并对模拟结果进行互相对比,得到了较好的结果.生活中很多时候两参数模型不能满足实际需要,所以我们在此基础上把模型推广到三参数下,并给出了参数的迭代公式,对成功概率参数选取问题做了说明.对后续处理一些数据缺失问题给予一定的帮助.
[Abstract]:Missing data generally exist in the field of experimental research and social investigation. The problem of missing data results in the analysis task and the inaccuracy of statistical results. How to deal with the missing data effectively, how to make full use of the data information, accurately reflect the characteristics of the research group, and achieve the expected research goal, has become a difficult and hot issue in the current statistical research. Because the missing data often contain some important information of the whole, if we want to apply the statistical analysis method to the field of processing missing data, the general idea is to fill in the incomplete data first, so as to get the complete data set. Then the data set is analyzed and the conclusion is obtained to accurately reflect the true situation. In this paper, for the data missing problem under the non-random deletion mechanism, under certain assumptions, the supplementary data are given by the method of probability and statistics, and the statistical inference of the distribution parameters is given by using the method of probability and statistics on the premise of certain assumptions. Then we give the quantile estimation of the probability distribution of complete data. We are more concerned with the median (0.5 quartile), the quartile (the 14th quartile / 0.25-quartile, respectively), the quartile, the quartile and the quartile. The third quartile, the 0.05 quartile, and the 0.95 quartile. At the same time, we estimate the parameter and quantile of Gamma distribution under the assumption that the probability of success is exponential distribution (parameter 位 can be given according to the parameter of Gamma distribution and the ratio of missing data). The iterative formula of parameters is given. In the stage of simulation research, R language is used to simulate the missing ratio of 1 / 10 / 1 / 5 / 2 / 2 / 3, and the simulation results are compared with each other and good results are obtained. In many cases, the two-parameter model can not meet the actual needs, so we extend the model to three-parameter model, and give the iterative formula of the parameters, and explain the problem of parameter selection of success probability. It is helpful to deal with some problems of missing data in the future.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
本文编号：2133593
[Abstract]:Missing data generally exist in the field of experimental research and social investigation. The problem of missing data results in the analysis task and the inaccuracy of statistical results. How to deal with the missing data effectively, how to make full use of the data information, accurately reflect the characteristics of the research group, and achieve the expected research goal, has become a difficult and hot issue in the current statistical research. Because the missing data often contain some important information of the whole, if we want to apply the statistical analysis method to the field of processing missing data, the general idea is to fill in the incomplete data first, so as to get the complete data set. Then the data set is analyzed and the conclusion is obtained to accurately reflect the true situation. In this paper, for the data missing problem under the non-random deletion mechanism, under certain assumptions, the supplementary data are given by the method of probability and statistics, and the statistical inference of the distribution parameters is given by using the method of probability and statistics on the premise of certain assumptions. Then we give the quantile estimation of the probability distribution of complete data. We are more concerned with the median (0.5 quartile), the quartile (the 14th quartile / 0.25-quartile, respectively), the quartile, the quartile and the quartile. The third quartile, the 0.05 quartile, and the 0.95 quartile. At the same time, we estimate the parameter and quantile of Gamma distribution under the assumption that the probability of success is exponential distribution (parameter 位 can be given according to the parameter of Gamma distribution and the ratio of missing data). The iterative formula of parameters is given. In the stage of simulation research, R language is used to simulate the missing ratio of 1 / 10 / 1 / 5 / 2 / 2 / 3, and the simulation results are compared with each other and good results are obtained. In many cases, the two-parameter model can not meet the actual needs, so we extend the model to three-parameter model, and give the iterative formula of the parameters, and explain the problem of parameter selection of success probability. It is helpful to deal with some problems of missing data in the future.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
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