11 Parameter estimation under multiply Type-II censoring

Abstract

This chapter discusses parameter estimation under multiply type-II censoring. It highlights the concept of best linear estimation, including best linear unbiased estimators, best linear invariant estimators, and Weibull distribution. It describes maximum likelihood estimation (MLE) in multiply Type H censoring and the large sample properties of MLE. In view of the fact that the MLE does not have a closed form, it is often tried to derive the approximate MLE. The approximate MLE can be easily derived for the location and scale family. In this family, instead of solving the likelihood equations directly, the linear terms of the Taylor expansions is applied so the likelihood equations become linear or quadratic equations and the closed forms of the solutions exist. The chapter also discusses the interval estimation for exponential distribution. It considers interval estimation for the parameters in exponential distribution under multiply Type II censoring. One-parameter and two-parameter exponential distributions are discussed in the chapter. For each parameter, three different confidence intervals are provided in the chapter, two approximate and one exact. The exact confidence interval can be used in most cases except some special situations.