记录值和记录值排序集抽样的统计推断
发布时间：2019-06-10 16:48
【摘要】：记录值是一种常见的数据表现形式,提出以来被广泛应用于气象学,水文学,体育赛事和寿命试验等领域,例如在水文学中每年同一时期的降雨量以记录值的形式出现;在体育赛事中某运动项目中不断刷新新的记录值等。记录值是顺序统计量的一种特殊形式。随着对排序集抽样研究的深入,发展起很多基于排序集抽样的抽样方案。结合记录值,人们提出了一种新的排序集抽样方法—记录值排序集抽样(Record RSS)。本文讨论了记录值样本和记录值排序集抽样下的统计推断问题,主要工作如下:(1)基于记录值样本,在极值分布模型下,讨论了参数的点估计和置信区间估计问题。在点估计问题上,导出了参数的极大似然估计和逆矩估计量。在区间估计问题上,讨论了参数的渐近置信区间和准确置信区间;在准确置信区间的建立方面,分别讨论了基于2?分布和F分布的构造方法,并讨论了两种方法下构造的枢轴量有解的存在唯一性。最后通过一个具体实例分析讨论的方法。(2)基于记录值排序集抽样,得到了Weibull分布参数的极大似然估计,利用极大似然估计的渐进正态性,考察了参数的渐进置信区间,也讨论了参数bootstrap法下参数的区间估计。在贝叶斯分析方面,考虑了Jeffreys和Reference先验作为无信息先验对参数进行客观贝叶斯统计推断。由于无法直接得到参数的贝叶斯估计的数值解,利用Metropolis-Hastings算法和Gibbs抽样解决问题。最后通过Monte-Carlo数值模拟对讨论的方法进行了对比分析。
[Abstract]:Recording value is a common form of data expression, which has been widely used in meteorology, hydrology, sports events and life testing. For example, the rainfall in the same period of each year appears in the form of recorded value in hydrology. Constantly refresh new record values in a sports event, etc. Record value is a special form of sequential statistics. With the deepening of the research on sort set sampling, many sampling schemes based on sort set sampling have been developed. Combined with record value, a new sampling method of sort set, record value sort set sampling (Record RSS)., is proposed. In this paper, the problem of statistical inference under the sampling of record value samples and record value sort sets is discussed. The main work is as follows: (1) based on the record value samples, under the extreme value distribution model, the problem of point estimation and confidence interval estimation of parameters is discussed. In the problem of point estimation, the maximum likelihood estimation and inverse moment estimation of parameters are derived. In the problem of interval estimation, the asymptotic confidence interval and accurate confidence interval of parameters are discussed, and the establishment of accurate confidence interval is discussed based on 2? The construction methods of distribution and F distribution are discussed, and the existence and uniqueness of the solution of the axis quantity constructed under the two methods are discussed. Finally, a concrete example is used to analyze and discuss the method. (2) based on the sampling of record value sort set, the maximum likelihood estimation of Weibull distribution parameters is obtained, and the progressive confidence interval of the parameters is investigated by using the asymptotic normality of maximum likelihood estimation. The interval estimation of parameters under parameter bootstrap method is also discussed. In the aspect of Bayesian analysis, Jeffreys and Reference priori are considered as non-information priori to carry out objective Bayesian statistical inference of parameters. Because the numerical solution of the parameter estimation can not be obtained directly, the Metropolis-Hastings algorithm and Gibbs sampling are used to solve the problem. Finally, the methods discussed are compared and analyzed by Monte-Carlo numerical simulation.
【学位授予单位】：成都信息工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
本文编号：2496587
[Abstract]:Recording value is a common form of data expression, which has been widely used in meteorology, hydrology, sports events and life testing. For example, the rainfall in the same period of each year appears in the form of recorded value in hydrology. Constantly refresh new record values in a sports event, etc. Record value is a special form of sequential statistics. With the deepening of the research on sort set sampling, many sampling schemes based on sort set sampling have been developed. Combined with record value, a new sampling method of sort set, record value sort set sampling (Record RSS)., is proposed. In this paper, the problem of statistical inference under the sampling of record value samples and record value sort sets is discussed. The main work is as follows: (1) based on the record value samples, under the extreme value distribution model, the problem of point estimation and confidence interval estimation of parameters is discussed. In the problem of point estimation, the maximum likelihood estimation and inverse moment estimation of parameters are derived. In the problem of interval estimation, the asymptotic confidence interval and accurate confidence interval of parameters are discussed, and the establishment of accurate confidence interval is discussed based on 2? The construction methods of distribution and F distribution are discussed, and the existence and uniqueness of the solution of the axis quantity constructed under the two methods are discussed. Finally, a concrete example is used to analyze and discuss the method. (2) based on the sampling of record value sort set, the maximum likelihood estimation of Weibull distribution parameters is obtained, and the progressive confidence interval of the parameters is investigated by using the asymptotic normality of maximum likelihood estimation. The interval estimation of parameters under parameter bootstrap method is also discussed. In the aspect of Bayesian analysis, Jeffreys and Reference priori are considered as non-information priori to carry out objective Bayesian statistical inference of parameters. Because the numerical solution of the parameter estimation can not be obtained directly, the Metropolis-Hastings algorithm and Gibbs sampling are used to solve the problem. Finally, the methods discussed are compared and analyzed by Monte-Carlo numerical simulation.
【学位授予单位】：成都信息工程大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1
【参考文献】
相关期刊论文 前6条
1 Liang Wang;Yimin Shi;Weian Yan;;Inference for Gompertz distribution under records[J];Journal of Systems Engineering and Electronics;2016年01期
2 王亮;师义民;常萍;;记录值样本下Burr XII模型的Bayes可靠性分析[J];火力与指挥控制;2012年08期
3 王炳兴;;Burr Type Ⅻ分布的统计推断[J];数学物理学报;2008年06期
4 雷刚,刘次华;定数截尾下极值分布的参数估计[J];应用数学;2005年S1期
5 程维虎;利用样本分位数的极值分布的参数估计[J];北京工业大学学报;2002年03期
6 王炳兴;;Weibull分布的统计推断[J];应用概率统计;1992年04期
相关硕士学位论文 前2条
1 程小宝;基于记录值的贝叶斯预测[D];兰州大学;2016年
2 任瑞静;排序集抽样下中位数的估计[D];华中师范大学;2014年
，本文编号：2496587
本文链接：https://www.wllwen.com/kejilunwen/yysx/2496587.html
