几种数据类型下两参数Logistic分布参数的近似极大似然估计

发布时间：2018-06-02 13:55

本文选题：Logistic分布 + 近似极大似然估计　；参考：《上海师范大学》2017年硕士论文

【摘要】：关于Logistic分布的研究最早可追溯到十八世纪,最初是为了解决如何模拟人口增长曲线的问题才提出的。后来的学者们在此基础上不断开拓研究,衍生发展出一系列Logistic分布的应用。本文所要研究的就是两参数的Logistic分布参数的估计问题。首先介绍Logistic分布相关的基本概念。同时,为了更全面的说明参数估计的方法,本文构建了几种不同的样本数据采集方式,分别是定数截尾、双边截尾、缺失数据。在这些样本数据下,首先是要分析了极大似然估计是如何计算的,发现这种情况下得到的超越方程很难求解,于是可以采用近似极大估计来进行参数的估计。并且运用数据模拟的方法对估计方法进行了实证分析。第一章是关于Logistic研究背景的介绍,以及Logistic分布国内外的研究进程。重点阐述了近代以来学者们对于Logistic分布的拓展应用和实践,以及不断发展的研究方法和理论创新。第二章到第四章就样本数据的采集方式的不同,详细分析定数截尾、双边截尾和缺失数据下的Logistic分布的参数估计各自的估计方法。并且就极大似然估计这种估计方法,具体讨论了它的理论,以及在极大似然估计的基础上,发展起来的近似极大似然估计。同时,各自推导了每种数据类型下近似极大似然估计的具体计算公式和估计效果计算公式。第五章则是对近似极大似然估计方法的实证运用,结合多种样本数据类型,进行数值计算。首先,运用林木平均直径数据验证估计效果,在得到估计效果良好的情况下,再次计算了在蒙特卡洛模拟数据下的参数估计情况,与真实值进行比较,从多方面综合评估此种估计方法的估计效果如何。
[Abstract]:The study of Logistic distribution dates back to the eighteenth century and was originally proposed to solve the problem of how to simulate the population growth curve. On this basis, scholars continued to explore and develop a series of applications of Logistic distribution. In this paper, we study the estimation of Logistic distribution parameters with two parameters. Firstly, the basic concepts of Logistic distribution are introduced. At the same time, in order to explain the method of parameter estimation more comprehensively, this paper constructs several different sample data acquisition methods, namely, fixed truncation, bilateral truncation and missing data. Under these sample data, it is necessary to analyze how the maximum likelihood estimation is calculated, and it is found that the transcendental equation obtained in this case is difficult to solve, so the approximate maximum estimation can be used to estimate the parameters. And use the method of data simulation to carry on the empirical analysis to the estimation method. The first chapter introduces the background of Logistic research and the research progress of Logistic distribution at home and abroad. This paper focuses on the development, application and practice of Logistic distribution by scholars since modern times, as well as the developing research methods and theoretical innovations. In the second to fourth chapters, the estimation methods of the parameters of the Logistic distribution under the deterministic truncation, the bilateral truncation and the missing data are analyzed in detail. The theory of maximum likelihood estimation and the approximate maximum likelihood estimation developed on the basis of maximum likelihood estimation are discussed in detail. At the same time, the formulas of approximate maximum likelihood estimation and estimation effect under each data type are derived respectively. The fifth chapter is the empirical application of the approximate maximum likelihood estimation method, combined with a variety of sample data types to carry out numerical calculations. First of all, using the tree average diameter data to verify the effect of the estimation, under the condition that the estimation effect is good, the parameter estimation under the Monte Carlo simulation data is calculated again, and compared with the real value. The effect of this method is evaluated from many aspects.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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