STATISTICAL INFERENCE FOR SOME CONTINUOUS DISTRIBUTIONS BASED ON RANKED SET SAMPLING

Abstract

McIntyre [54] proposed ranked set sampling (RSS) as a sampling method that improve the precision of the sample mean estimator of the population mean without the bias of researcher choice and referred to it as a method of unbiased selective sampling using ranked sets. Subsequently some prop-erties of RSS estimator of population mean such as unbiasedness, variance and relative precision with respect to simple random sampling (SRS) have been established by Takahasi and Wakimoto [68].

The aim of this thesis is to describe the structural method for obtain-ing RSS and study the statistical inference for some continuous distribution based on the two sampling methods; RSS and SRS.

This thesis consists of six chapters:

Chapter 1

This chapter is an introductory chapter. It consists of de nitions and basic concepts which will be used in this thesis. At the end of this chapter, a literature review of the previous studies is presented.

Chapter 2

In this chapter, we provide Bayesian estimation for the parameters of the Pareto distribution based on SRS and RSS. Posterior risk function of the derived estimators are also obtained by using squared error loss (SEL) function. Two-sample Bayesian prediction for future observations are ob-tained by using SRS and RSS. Lastly, a simulation study is conducted to assess the performance of the proposed estimation and prediction techniques. The results of this chapter were published at:

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Summary

" Journal of Statistics Applications & Probability, 2015, 4 (2), 1{11."