Ratio Estimation Of The Population Mean Under The Optimal Sampling Design

As we all know,an important part of in statistical cognition activities is to obtain statistical data through statistical surveys,and then scientific statistical analysis.In practical problems,when the set size is large,to obtain all the required data is not easy,or impossible to achieve,which gives us to study the characteristics of population is difficult.the application of sampling technology is a good solution to this problem,we don't have to get all the individual infor-mation,but the use of sample population.A good sampling method can save the cost of investigation,enhance the timeliness of the investigation,help improve the quality of the data,undertake the task of a comprehensive survey is diffi-cult,the sample can describe the population characteristics well.The method of ranked set sampling(RSS)provides an effective way to achieve observation-al economy in terms of precision achieved per unit of sampling.Initially the concept of RSS was introduced by McIntyre(1952)to estimate pasture yields as an effective tool,especially when ranking the units in a small set is easy and inexpensive,the advantages of RSS are more obvious.In order to reduce the error of ranking and keep optimality inherited in the original RSS procedure,Samawi et al.(1996)and Al-Odat et al.(2001)introduced a modification of RSS called extreme RSS(ERSS)and moving ERSS(MERSS).After the introduction of these two sampling methods,statisticians have carried out a more indepth study of many commonmodels.This paper studies the ratio estimation of the population mean under RSS,ERSS and MERSS,and the main contents are divided into the following aspects:(1)The ratio estimation of the population mean was estimated after us-ing the first or the third quartile information of the auxiliary variables under RSS.The simulation results show that the ratio estimations under RSS are significantly more efficient than the ones under simple random sampling.(2)The ratio estimation of the population mean under ERSS was studied.The nature of this ratio estimate is obtained.The simulation results show that the ratio estimations under ERSS are significantly more efficient than the ones under simple random sampling.(3)The ratio estimation of the population mean was estimated after using the first or the third quartile information of the auxiliary variable under ERSS.The nature of this ratio estimate is obtained.The simulation results show that the ratio estimations under ERSS are significantly more efficient than the ones under simple random sampling.(4)The ratio estimation of the population mean was estimated after us-ing the first or the third quartile information of the auxiliary variables under MERSS.The nature of this ratio estimate is obtained.The simulation results show that the ratio estimations under MERSS are significantly more efficient than the ones under simple random sampling.