Approximate Maximum Likelihood Estimation Of Two-parameter Logistic Distribution Parameters Under Several Data Types

Research on the Logistic distribution can be traced back to the 18 th century.Originally,The Logistic distribution is supposed to solve the problem of how to simulate population growth curve.As time goes on,the use of Logistic distribution is expanded to more broader domains on the basic of population growth research.The main objective of this article is studying the problem about parameter estimation for Logistic distribution of two parameters.Firstly,introduce the related basic concept of Logistic distribution.At the same time,to comprehensive explanation of the parameter estimation method better,designing several different ways of acquisition methods for sample data.Specifically,the patterns are type ii censoring,bilateral truncated,missing data.With this sample data,first step is to analyze how to estimate parameters by maximum likelihood estimation.However,it is hard to solve the transcendental equation of maximum likelihood estimation.so we consider to take other more easier way,like approximate maximum likelihood estimator.Hence,that is the main subject of this paper.The introduction of the first chapter is about the Logistic research background and the research history of Logistic distribution at home and abroad.This paper put emphasis on the modern scholar's research results about the application and practice of Logistic distribution.Certainly,there are many developments and theoretical innovation of the Logistic distribution.The second chapter to the fourth chapter are the introductions of the approximate maximum likelihood estimation method apply to three different styles sample data.The three styles of sample data are truncated data with definite numbers,bilateral truncated data and missing data.All the sample data are subject to Logistic distribution.In those chapters,detailed discussing of its theory,and the specific calculation of the maximum likelihood estimation method with three different types sample data.The fifth chapter is about the empirical analysis for approximate maximum likelihood estimation method.On the one hand,test the estimation effect for average diameter data of forests.On the other hand,use approximate maximum likelihood estimation method to test Monte Carlo simulation data.Finally,take all the analyze results to more intuitive understand the parameter estimates method.