Parameter Estimation For Two-Parameter Rayleigh Distribution Based On Censored Data

Censored data often occurs in survival analysis and reliability theory. In recent years,Many authors considered Type-II censored data, progressive censored and hybrid censored data in the literature. In this thesis, we discuss the parameter estimation of two parameter Rayleigh distribution with the consideration of censored data and study the problem of the following aspects:Firstly, this paper discusses the estimation of scale parameter from two parameter Rayleigh distribution under type II censored data when the location parameter is known, and obtain Maximum likelihood estimation, bayes estimation, E-Bayes estimation of parameter and properties of several E-Bayes estimation. Comparing the bias and mean square error of several estimates using the method of numerical simulation that proves out E-Bayes estimation method behaves better than bayes estimation.Secondly, this paper considers bayes estimation of parameters from two parameter Rayleigh distribution based on square loss function and LINEX loss function under progressive type II censored data. Due to its complicated form, we provide an approximate method to derive analytical form of estimates. Comparing the bias and mean square error of estimates using the method of numerical simulation, it turns out that Bayes estimation behaves better than Maximum likelihood estimation.Finally, this paper discusses bayes estimation of parameters from two parameter Rayleigh distribution under type II hybrid censored data. Because it has no exact expression, we use Lindley approximate method and MCMC method to solve out the numerical solution. After a numerical simulation analysis, we find out bayes estimation method has a high accuracy and the result using Lindley approximate method is slightly better than the result using MCMC method.