Classical And Bayesian Estimation For Generalized Exponential Distribution And Generalized Inverted Exponential Distribution Based On General Progressive Type-? Censored Data

Survival analysis is a statistical method that be used in a variety of industries.For example,in manufacturing,it is used to analyze lifetime of machine.In the case of finance,it is used to analyze the time to repay the home mortgage.In the case of the insurance industry,it is applied to the time required for the expiration of insurance and securities rights.But,due to the character of the survival analysis using data generated according to the passage of time,it is difficult to obtain complete data.So,in the survival analysis,censoring data is used frequently.In this paper,we introduce the recently most frequently used Progressive Type-? censored samples data among many types of censored data.Especially,General Progressive Type-II censored data includes the Progressive Type-II censored data,the Type-II censored data and the Doubly Type-II censoring data.Therefore,more flexi-bility and adaptability than other data.We also introduce the Generalized Exponential distribution and the Generalized Inverted Exponential distribution which are widely used in lifetime prediction and reliability analysis.Also,we analyze the significance of parameter estimation under several models and discuss the suitability of the Gener-alized Inverted Exponential distribution and General Progressive Type-II censored data in survival analysis.In this study,we deal with the estimation of two parameters of the Generalized Ex-ponential distribution and the Generalized Inverted Exponential distribution based on General Progressive Type-II censored samples.This paper totally consists of 6 parts:The chapter 1 introduces Exponential distributions and related Generalized Exponen-tial(GE)distribution and Generalized Inverted Exponential(GIE)distribution.Also,It summarizes various censoring data:The chapter 2 studies the estimations of General-ized Exponential distributions under Progressive Type-? censored data.It derives the Maximum Likelihood estimation and the Bayes estimation using the statistical software R.The Bayes estimators are obtained based on Metropolis-Hasting sampling method under squared error loss function:The chapter 3 considers the estimations of Gener-alized Exponential distributions based on General Progressive Type-II censored data.It presents MLEs(maximum likelihood estimators)and Bayes estimators using the sta-tistical software R.And it compares with the Progressive Type-? censored data in the chapter 2 through simulation study using R:The chapter 4 discusses the estimations of Generalized Inverted Exponential distributions based on General Progressive Type-?censored data.It derives MLEs,Asymptotic confidence intervals and Bayes estima-tions:The chapter 5 deals with two real data sets to test suitability of the distribution and data:The Chapter 6 concludes this paper.