Parameter Estimation Of Pareto Distribution Based On Ranked Set Sampling

In this article,we are interested in estimation of the scale and the shape pa-rameters for pareto distribution p(?,?).Simple random sampling(SRS),ranked set sampling(RSS),extreme RSS(ERSS)and median RSS(MRSS)will be used.An unbiased estimator(UE),a modified UE(MUE),the best linear unbiased estima-tor(BLUE(s)),the modified BLUE(s)(MBLUE(s))and ad hoc estimators(AHEs)of ? and a from p(?,?)will be respectively studied in cases when one parameter is known and when both are unknown.We compare these estimators under perfect and imperfect ranking.In the following,let us introduce the contents of each chapter in brief.Chapter 1 summarizes some related background of Pareto distribu-tion and ranked set sampling,and the main work and innovation of this dissertation.Chapter 2 mainly studies the parameter estimation of Pareto distri-bution based on RSS.Several estimators of the scale and shape parameters from pareto distribution will be considered in cases when one parameter is known and when both are unknown under RSS.These estimators contains UE,MUE,BLUE(s),MBLUE(s)and AHEs.Chapter 3 mainly studies the parameter estimation of Pareto distri-bution based on ERSS.Several estimators of the scale and shape parameters from pareto distribution will be considered in cases when one parameter is known and when both are unknown under ERSS.These estimators contains UE,MUE,BLUE(s),MBLUE(s)and AHEs.Chapter 4 mainly studies the parameter estimation of Pareto distri-bution based on MRSS.Several estimators of the scale and shape parameters from pareto distribution will be considered in cases when one parameter is known and when both are unknown under MRSS.These estimators contains UE,MUE,BLUE(s),MBLUE(s)and AHEs.Chapter 5 according to the theoretical results of Chapters 2,3 and 4,the efficiency of the corresponding estimator under perfect ranking and imperfect ranking is calculated.Chapter 6 summarizes the dissertation and prospects in the future work.