Parameter Estimation For Rayleigh Distribution Based On Progressive Type-? Interval Censored Data

With the perfection of the basic theory on Censored Data, and the needs of practical application, mechanism of Progressive Type-II Interval Censoring is proposed, however, in practical application Rayleigh distribution model is a distribution model that is the most common one. This paper discusses the parameter estimation of Rayleigh distribution model in the Progressive Type-II Interval Censoring occasion. The main parts of the research can be demonstrated as follows:Firstly, discuss the computing problem of the parameter ? of Rayleigh distribution model and Maximum Likelihood Estimation of parameter p of extracting experimental individual number R based on Progressive Type-II Interval Censoring,finding that the Maximum Likelihood Estimation of parameter ? cannot be directly worked out through expression by using the traditional method. As a result, the author applies Newton-Raphson iteration method to obtain the approximate solution of estimated value of the parameter ?.Secondly, according to condition and theorem that the related literature needs to be satisfied, it proves that the congruence and asymptotic normality of Maximum Likelihood Estimation of parameter ?, which indicates that the Maximum Likelihood Estimation is still of convergence through iteration Newton-Raphson approximation method.Thirdly, discuss Rayleigh distribution under Bayesian Estimation problem of the Square Loss Function. When Bayesian Estimation cannot figure the estimated value out simply and accurately, we can take advantage of Lindley approximation method to get its numerical solution. And caculate the mean deviation and mean squared error under Maximum Likelihood Estimation method and Bayesian Estimation method through the Numerical Simulation, and then compare and analyze them to draw the conclusion.