الفهرس 
order statisticsOnly 14 pages are availabe for public view
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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:
” Journal of Statistics Applications & Probability, 2015, 4 (2), 1{11.”
Chapter 3
Chapter 3 presents order statistics of independent and non identically distributed (INID) random variables to obtain ordered ranked set sampling (ORSS) under Type-II censoring scheme. Bayesian inference of unknown parameters under a SEL function of the Pareto distribution are determined. We compute posterior risk function of the derived estimators based on ORSS and compare them with those based on the corresponding SRS to assess the e ciency of the obtained estimators. Two-sample Bayesian prediction for future observations are introduced by using SRS and ORSS. A simulation study and real data are applied to show the accuracy of the proposed results. The results of this chapter were published at:
”Communications in Statistics Theory and Methods, 2017, 46 (13), 6264{ 6279.”
Chapter 4
The aim of this chapter is to use RSS to develop Bayesian analysis based on upper record statistics values. Bayes estimations of SEL and linear expo-nential loss (LINEX) functions and maximum likelihood estimation (MLE) are derived for linear exponential distribution based on SRS and record ranked set sampling (RRSS). These estimators are compared via their bias and mean squared error (MSE). A simulation study and real data are carried out to study the precision of MLE and Bayesian estimations for the param-eters involved. The results of this chapter were accepted for publication at:
”Journal of Mathematics and Statistics, to appear.”
Chapter 5
In this chapter, we use ORSS from order statistics of INID random vari-ables to obtain Bayesian estimation for the scale parameter of Rayleigh distribution under Type-II doubly censoring scheme. This is done with re-spect to both SEL and Al-Bayyati loss functions (ALF). We obtain MSE and bias of the derived estimators based on ORSS and compare them with those based on the corresponding SRS to appreciate the e ciency of the obtained estimators. Furthermore, we present the two-sample Bayesian pre-dictive density function (point and interval) for the ordered future sample. Finally, a simulation study and real data are conducted to assess the perfor-mance of the theoretical results. The results of this chapter were accepted for publication at:
”American Journal of Statistics and Probability, to appear.”
Chapter 6
In this chapter, order statistics of INID random variables are used to obtain ORSS. Recurrence relations for single and product moments are ob-tained from Kumaraswamy generalized distribution based on ordinary order statistics. The Kumaraswamy generalized distribution has a large num-ber of well known lifetime special submodels such as the Kumaraswamy Weibull, Kumaraswamy log-generalized inverse Weibull and Kumaraswamy generalized Rayleigh distributions, among others. The Kumaraswamy log-generalized inverse Weibull distribution is given as an application to obtain best linear unbiased estimators (BLUEs) of the location and scale parame-ters using ORSS and SRS. The relative e ciency of the derived estimators are obtained to compare (BLUEs) based on ORSS (BLUEs-ORSS) with BLUEs-SRS. We show that BLUEs-ORSS are better than BLUEs-SRS for the location and scale parameters of Kumaraswamy log-generalized inverse Weibull distribution. The results of this chapter were submitted to an in-ternational statistical journal.