-
摘 要 数理统计里面最重要的问题是统计推断。 统计推断是基于样本的总体分布或分布特性的数量等等的统计方法，在统计推断的过程中需要用到参数估计。参数估计是数理统计的重要组成部分，它是一种从样本来估计未知参数的方法。随着概率论思想在实际生活中的应用越来越广泛， 参数估计的运用在各个领域的作用都凸显了出来。在已知系统模型结构时，我们用系统的输入和输出数据计算系统模型参数的时候可以用到参数估计。 如在两种物品服从方差相等的正态分布且相互独立时，求置信水平为某一个值的置信区间。18 世纪末，德国数学家 C.F.高斯首先提出参数估计的方法，他用最小二乘法（它是参数估计的一种方法）来计算天体运行的轨道。此篇论文主要研究的是参数估计的几种方法的优缺点。参数估计包含点估计和区间估计，我们主要介绍点估计与区间估计的相同点和不同点。计算点估计的基本方法有两个，一个是矩法估计，另一个是最大似然估计法。点估计的这两个方法我们需要求同存异，这也是本文将要探讨的重点内容。我们旨在以后对参数估计进行更深刻的领悟，工作运用上更加灵活。62339
- 上一篇：Fisher信息量及简单应用
- 下一篇：经济问题中的相关分析与回归分析
毕业论文关键词： 点估计；矩法估计；最大似然估计；区间估计
Abstract Statistical inference is the core problem of mathematical statistics. Statistical inference is astatistical method basing on the population distribution of the sample or the number of thedistributed characters etc. Parameter estimation may be used in the process of statisticalinference. Parameter estimation is the important component of mathematical statistics, andis a method estimating unknown parameter from the sample.With more and more wide application of probability theory thinking in the real life, theapplication of parameter estimation has highlighted in every field. Under knowing systemstructure, we may use parameter estimation to calculate system parameter by the systeminput and output data of parameters of process. For example, when the two items areknown about obeying normal distribution, equal variance and being independent each other,we may solve the confidence interval of a certain value. In the end of the 18th century,German mathematician C.F. gauss first put forward the method of parameter estimation, heuses the least square method (it is a method of parameter estimation)calculating celestialbody's orbit.This paper mainly studies the advantages and disadvantages of several methods ofparameter estimation, parameter estimation which contains the point estimation andinterval estimation. We mainly introduces the point estimation and interval estimation ofthe same and different, and the basic methods of calculating point estimation has two, oneis the torque estimation, the other is the maximum likelihood estimation method, pointestimation of the two methods we need to seek common ground while putting asidedifferences, this also is the main content of this article will explore. We study parameterestimation to understand the future of the parameter estimates more profoundly, and applyit to the practice more flexibly.
Keywords: Point estimation; Moment method; Maximum likelihood estimation;Interval estimation.
目 录
第一章 绪 论..1
1.1研究背景1
1.2研究意义1
1.3论文的结果安排... 1
第二章点估计.. 2
2.1 点估计的概念.. 2
2.3最大似然法估计... 2
2.4据估计法与最大似然法的比较..3
第三章区间估计..6
3.1区间估计的概念... 6
3.2区间估计的定义... 6
3.3常见正态总体的参数估计.. 6
3.4常见非正态总体的参数估计11
第四章 点估计与区间估计的比较 13
4.1 点估计与区间估计的比较... 13
结 论...14