Theory,Method And Applications Of Statistical Inference For The Type ? Generalized Logistic Distribution

The Logistic Distribution(LD)function is often used as a model for the growth curve and the binary response variable.The density curve of the distribution has position,scale parameters,and the shape is similar to the shape of the normal distribution,but the tail is thicker.For better description,the shape of the tail of the data distribution often introduces two shape parameters,and the generalized Logistic Distribution(GLD)is obtained.As a kind of skewed distribution,GLD has a skewness and kurtosis coefficient that can be changed within a certain range,and can be more flexibly used in the fields of biology,economy,environment and engineering.At present,people have paid more and more attention to the research of GLD.So far,the research on GLD has achieved a series of results,but mainly focus on the research of type I GLD.There are few studies on type ? GLD and not deep enough.There are five forms of GLD,namely:type ?,type ?,type ?,type ? and type ?.Compared with other types of GLD,type ? GLD introduces two shape parameters,which are more flexible and can effectively describe actual data.So it has research significance and application value.Therefore,we mainly studies the statistical inference problem of type ? GLD in this thesis(abbreviated as GLD_?).In this thesis,we study the general properties and order statistics of GLD_?.First,sys-tematically combing the nature of GLD_? to pave the way for subsequent research.Since the distribution function of GLD_? is more complicated,it is difficult to directly calculate the over-all digital features and properties,so this thesis gives two methods to construct GLD_?:one is a construction method based on Gamma distribution;one is a construction method based on Beta distribution,and uses the latter to infer the nature of GLD_? is more convenient.In order to study GLD_? with two shape parameters better,this thesis gives the asymptotic distribution of GLD_?:extreme value distribution,when two shape parameters approach infinity respec-tively.This property fully illustrates the relationship between GLD_? and the extreme values distribution;Secondly,the order statistic theory plays an important role in statistical inference,especially in the subsequent parameter estimation.Therefore,this thesis uses a certain length to discuss the order statistic of GLD_?.In this thesis,we give the distribution function of order statistic and its various moments for GLD_?.It is proposed to use the maximum and minimum order statistics to derive the relation of each moment,which can be extended to other distribu-tions with certain applicability.In addition,we discusses the parameter estimation problems for GLD_? in this thesis.At present,the existing parameter estimation methods for GLD_? have two estimation methods:moment estimation and maximum likelihood estimation.We give the asymptotic normality and proof of the moment estimator of GLD_?.However,these two estimation methods have certain limitations,such as:the moment estimation is too dependent on the samples,and can not fully utilize the sample information.Therefore,in addition to the moment estimation and the maximum likelihood estimation,the L-moment estimation and the probability weighted moment estimation are given.Using these four estimation methods to estimate the parameters of GLD_?,and numerical simulations are carried out to compare the superiority of various estimates.