Statistical Inference Of The Generalized Logistic Distribution Under Type-Ⅱ Censoring

The generalized Logistic distribution (GLD) was first explicitly introduced by Bal-akrishnan and Leung in 1988, GLD was further studied by many researchers. It was one of distributions with location, shape and scale parameters. As generalization of the L-ogistic distribution, not only have the location and scale parameters, but also have the shape parameter that can affect the skewness and kurtosis, is a kind of skewed distribu-tion. It widely used in many fields. There are five types of the distribution. This article main research statistical inference of the type-Ⅰ GLD under type-Ⅱ censoring.In this thesis, we mainly discuss with the parameter estimation of the three-parameter GPD. While traditional methods, such as the methods of moments (MOM), the probability weighted moments (PWM) and the maximum likelihood (ML) have been extensively applied, there are several problems and limitations when they are used. The ML method may be inapplicable whenever the algorithm used for estimating the parameters fails to converge. Most of those methods provide estimators for full ob-servation, but censored data often appears. Estimating methods with censored data are different from full observation. Even about censored sample parameter estimation method, most are made of type-V GLD. To solve these problems, this article studies the moments estimation, probability weighted moments estimation, L-moments estima-tion, LH-moments estimation and maximum likelihood estimation under the full sam-ple. Then partial probability weighted moments estimation and maximum likelihood estimation under type-Ⅱ censored sample were derived in this ariticle. Furthermore, we compare the estimation precision among those estimated methods by Monte Carlo simulation.In addition, this thesis studies the record values of type-Ⅰ GLD. Main properties of the lower record values of type-Ⅰ GLD, as well as how to estimate parameter by lower record values. This thesis gives the best linear unbiased estimation of the location parameter μ and scale parameters σ. In addition, also gives the best linear unbiased prediction of unobserved lower record values through observed data. Then this thesis studies the estimation and prediction effect through data simulation.