Statistical Inference Of Unknown Parameters For Generalized Exponential Distribution Under Progressive Type-? Censoring Scheme

At present,the survival analysis of products based on censored data has been paid much more attention.The statistical inference under progressive type-? censoring data is a research hotspot in recent years,and the results are widely used in engineering reliability research.The paper mainly discusses statistical inference of unknown parameters for gen-eralized exponential distributions under progressive type-? censoring schemes.This paper introduces the history and development of progressively eensored data,discusses the advantages and disadvantages of different censored schemes.The paper also in-troduces the generalized exponential distribution and the stress strength model in en-gineering,and analyzes the significance of reliability parameter estimation under the generalized exponential model.The paper are arranged as follows:the first chapter introduces the research back-ground and research status of statistical inference of parameters based on progressively Type-? censored data.The second chapter introduces what the progressively Type-?censored data is and the properties of the generalized exponential distribution.The third chapter considers the estimation of the scale parameter of the generalized expo-nential distribution under progressively type-? censored data when the shape parameter is known.The estimation of R=P(Y<X)when X and Y are independent general-ized exponential random variables with different scale parameters and the same shape parameter based on progressive type-? eensoring samples are studied in chapter four.In this chapter,the maximum likelihood estimator(MLE)and approximate maximum likelihood estimator(AMLE)of the parameter R are obtained.Moreover,the Bayes estimation using the Gibbs method and Metropolis-Hasting procedure are derived.A Monte Carlo simulation and an analysis of two real data sets are presented to evaluate the various proposed methods.The fifith chapter summarizes the paper and presents what should do in the future.