Parameter Estimation And Its Numerical Simulation Of Two-parameter Generalized Exponential Distribution

Since Gupta and Kundu argued two-parameter generalized exponential (GE)distribution, it has caused the attention of many scholars and they research it widely. Thisdistribution can better fit some life data, and is widely used in many fields.Many scholarsstudy on the parameter estimation and its property of GE distribution, but they mainlystudy in a single case under the same loss function.Under different loss functions,theparameter estimation of GE distribution is less discussed,especially the study on theE-Bayes estimation and hierarchical Bayes estimation is very few.On the basis of predecessors’ research, this paper introduce GE distribution in thewhole sample type censored-I data model, we consider different situations, with differentloss functions, discuss E-Bayes estimation and hierarchical Bayes estimation, and with theMonte Carlo simulation. In the first chapter,we introduce the present situation, the modeland the main work. In the second chapter, we introduce the theory of Bayes statistics, therelated theorem and definitions. In the third chapter, when λ is known, we give the MLE,the Bayes estimation、E-Bayes estimation and hierarchical Bayes estimation of α and Runder two different loss functions, with MC simulation we find that the error of theparameter estimation is smaller under LINEX loss function, and E-Bayes estimation andhierarchical Bayes estimation effect well. In the fourth chapter, when α and λ areunknown, the MLE of α and λ are given, with Lindley approximation theorem we get theBayes estimation of α and λ, in the last section, through the MC simulation, we find theeffect is better under the square loss function. In the end,the full text is summarized, wepoint out the merit and shortcoming and we further prospect the paper.