Statistical Inference For The Type Ⅳ Generalized Logistic Distribution

Statistical models are usually used in the fields of finance,sociology and biomedicine,etc.Statistical distribution plays an important role in modeling.Logistic distribution is widely used for describing growth curve models and biochemical reaction curves and so on.But there are usually some limitations of Logistic distribution in modeling due to its symmetric heavy tail.So it is necessary to introduce shape parameters to fit asymmetric or thin-tailed data.Type ⅣGeneralized Logistic Distribution（GLDIV）is a generalization of Logistic distribution,which is by introducing two shape parameters to make distribution more flexible.The aim of this dissertation is to discuss the statistical inference of GLDIV.Firstly,we introduce the construction and properties of GLDIV,including the influence of the change of two shape parameters on the distribution,numerical characteristics and calculation of order statistics,etc.Then,parameters estimation of GLDIV under complete samples is discussed with four kinds of estimation methods,which include Methods of Moments（MOM）,Improved TL-Moments（ITLM）,Improved Probability Weighted Moments（IPWM）and Improved LH-Moments（ILHM）.The performance of last three methods are compared by simulation.The results show that methods of ITLM and IPWM perform better,especially when the sample size is large,the estimation bias and mean square error are both relatively small with the method of ITLM.Next,the parameter estimation with EM Algorithm（Expectation Maximization Algorithm）in the case of progressively censoring data is discussed.The results of simulation show that the estimation bias and mean square error are both small when the censoring ration is small and q=1.5.As the censoring ratio increases,the estimation bias and mean square error gradually increase,but the estimation bias and mean square error are relatively small when the shape parameter q is small（q=0.5）.Finally,three goodness of fit test statistics for GLDIV are given,including AD（AndersonDarling）test statistic,CV（Cramer-von Mises）test statistic in EDF（Empirical Distribution Function）type tests,and the test statistic based on Box-Cox transformation.The test critical value table under different sample size is given.Furthermore,simulation is employed for accessing the power of the three test statistics.The results show that the test power of BCn2 is higher when the skewness of distributions in the null hypothesis and alternative hypothesis is equal,otherwise,the test power of An2 is higher.