Statistical Inference Of The Type-??Type-??Mixture Of Type-? Generalized Logistic Distribution

Since generalization of the Logistic distribution (LD) was put forward in 1988, the generalized Logistic distribution (GLD) have been done a lot of researches by a large number of scholars. It has three parameters, namely location, shape and scale parameter. According to the composition of the parameters, there are five types of distribution. Currently, GLD has been widely used in survival analysis, quantitative biology and so on, however, most of the research findings are based on the type-I GLD. Even though type-II GLD and type-IV GLD have been applied considerably in these area, there are few studies pertaining to them. Therefore, it is significantly important to conduct a research on this topic from both theoretical and practical perspectives. This master dissertation mainly discusses statistical inference of the type-II GLD?type-IV GLD and mixed distribution by two type-I GLDs.Firstly, we study the properties of type-II GLD, and discuss the parameter estima-tions, several estimation methods of parameters are given in my dissertation, such as the traditional methods of moments (MOM), the probability weighted moments (PWM), L-moment and trimmed L-moment by using order statistics. Secondly, estimation methods of parameters will be contrastively studied according to the simulation results. Thirdly, the type-IV GLD can transform to LD, type-? GLD, type-? GLD, type-? GLD by selecting different parameters. Therefore, it is very important and meaningful to discuss special properties of type-IV GLD. Fourthly, statistic properties, method of parameter estimation and simulation generation method of type-? GLD will be discussed in this master dissertation.In addition, application background and characteristic based on mixed distribution by two type-? GLDs are considered. Moreover, EM algorithm for L-moment estimation of mixed distribution by two type-? GLDs and estimation effect through simulation study are given.