Estimation In The Location-Scale-Shape Of Type ? Generalized Logistic Distribution

The Generalized Logistic Distribution(GLD) is a generalization of the Logistic Distribu-tion. The importing of shape parameter makes it a skewed distribution, which can fit the practical data effectively. This distribution has been widely used in various fields. GLD has five types. In the dissertation, we mainly study the location-scale-shape model of type I generalized logistic distribution, which is the most widely used distribution.This dissertation mainly researches the estimation problem of GLDI, which is divided into four parts:the first part is about the research significance and research status of GLDI at home and abroad; The second part introduces the definition and the properties of GLDI; In the third part, the moment method and generalized moment methods(such as probability weighted mo-ment method, L-moment method, TL-moment method) are applied in the parameter estimation of GLDI. The existence and uniqueness theorem of all kinds of moment methods is also pre-sented. At the same time, Monte Carlo method is used to compare all the moment methods; The forth part:the Maximum Likelihood Estimation, the Quantile Estimation and Mixture Estima-tion are given, and a simulation study about them is carried out.In particular, when summarizing the advantages and disadvantages of various estimation methods, this dissertation also takes the existence, uniqueness and large sample properties of various moment estimation into account. The article using the Quantile method to study the parameter estimation of the GLDI, has not been found. But we give the Quantile Estimation for GLDI in the dissertation, using Expectation-Conditional Maximization(ECM) algorithm. In addition, Mixed Estimation method is proposed, that uses the maximum likelihood estimation and the Quantile Estimation. The Mixed Estimation method improves the estimation effect of location and scale parameter. By using recursion method, this dissertation gives the expectation, variance and covariance of GLDI's order statistics. In the end, the simulation study of various estimators is given under different sample sized and different shape parameter.