Estimation For The Pareto Distribution Under Progressive Type ⅡInterval Censored Data

This thesis concerns with the estimation problem for the Pareto distribution based on progressive Type-11interval censoring with random removals. We first discuss the maximum likelihood estimation of the model parameters. Then, we show the consistency and asymptotic normality of maximum likelihood estimators based on progressive Type-Ⅱ interval censored sample. Finally, a numerical simulation experiment is presented to illustrate the application of the results under this censoring scheme.This thesis is organized as follows. In Chapter1, we give the definitions and properties of various censoring schemes and the Pareto distribution. In addition, we provide an overview of various developments that have taken place in this direction. In Chapter2, we discuss the maximum likelihood estimation for the Pareto distribution based on the progressive Type-Ⅱ interval censored sample, and obtain the iterative expression by using the Newton-Raphson method. The consistency and asymptotic normality of maximum likelihood estimators based on this censored sample are shown in Chapter3. And in Chapter4, a numerical simulation experiment is given to demonstrate the results obtain in this thesis are correct.