本文選題：Logistic分布 + 近似極大似然估計��； 參考：《上海師范大學》2017年碩士論文

【摘要】：關于Logistic分布的研究最早可追溯到十八世紀,最初是為了解決如何模擬人口增長曲線的問題才提出的。后來的學者們在此基礎上不斷開拓研究,衍生發(fā)展出一系列Logistic分布的應用。本文所要研究的就是兩參數(shù)的Logistic分布參數(shù)的估計問題。首先介紹Logistic分布相關的基本概念。同時,為了更全面的說明參數(shù)估計的方法,本文構建了幾種不同的樣本數(shù)據(jù)采集方式,分別是定數(shù)截尾、雙邊截尾、缺失數(shù)據(jù)。在這些樣本數(shù)據(jù)下,首先是要分析了極大似然估計是如何計算的,發(fā)現(xiàn)這種情況下得到的超越方程很難求解,于是可以采用近似極大估計來進行參數(shù)的估計。并且運用數(shù)據(jù)模擬的方法對估計方法進行了實證分析。第一章是關于Logistic研究背景的介紹,以及Logistic分布國內外的研究進程。重點闡述了近代以來學者們對于Logistic分布的拓展應用和實踐,以及不斷發(fā)展的研究方法和理論創(chuàng)新。第二章到第四章就樣本數(shù)據(jù)的采集方式的不同,詳細分析定數(shù)截尾、雙邊截尾和缺失數(shù)據(jù)下的Logistic分布的參數(shù)估計各自的估計方法。并且就極大似然估計這種估計方法,具體討論了它的理論,以及在極大似然估計的基礎上,發(fā)展起來的近似極大似然估計。同時,各自推導了每種數(shù)據(jù)類型下近似極大似然估計的具體計算公式和估計效果計算公式。第五章則是對近似極大似然估計方法的實證運用,結合多種樣本數(shù)據(jù)類型,進行數(shù)值計算。首先,運用林木平均直徑數(shù)據(jù)驗證估計效果,在得到估計效果良好的情況下,再次計算了在蒙特卡洛模擬數(shù)據(jù)下的參數(shù)估計情況,與真實值進行比較,從多方面綜合評估此種估計方法的估計效果如何。
[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.
【學位授予單位】：上海師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.1

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相關期刊論文 前4條

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2 程維虎;基于Logistic總體Ⅱ型截尾樣本分布參數(shù)的極大似然估計[J];北京工業(yè)大學學報;2004年01期

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本文編號：1969005