Optimal Estimation Of Location And Scale Parameters Under Moving Extreme Ranked Set Sampling

Obtaining statistical data is an indispensable part of statistical inference.In practical problems,due to the experimental cost,experimental scale or other constraints,exact measurement of a selected unit is either difficult or costly and time-consuming.In response to this situation,McIntyre(1952)first proposed sorted set sampling(RSS)in estimating forage yield.RSS is a economical and efficient method of data collection,especially when interest variables are difficult to quantify but easy to rank.However,the accuracy of the ordering will affect the efficiency of the estimation.In order to reduce the error of ranking and keep optimality inherited in the original RSS procedure,Al-Odat et al.(2001)introduced a modification of RSS called moving extremes RSS(MERSS).After the introduction of this sampling method,statisticians have carried out a more indepth study of many commonmodels.This paper studies the parameter estimation of the location-scale family under MERSS,and the main contents are divided into the following aspects:(1)The best linear unbiased estimators(BLUEs)of parameters in the Location-scale family under MERSS was studied.The numerical results show that the BLUEs under MERSS are significantly more efficient than the ones under SRS.(2)The best linear invariant estimators(BLIEs)of parameters in the Location-scale family under MERSS was studied.The numerical results show that the BLIEs under MERSS are significantly more efficient than the ones under SRS.(3)The BLUE and BLIE of population mean in the Location-scale family under MERSS was studied.The numerical results show that the BLUE and BLIE under MERSS are significantly more efficient than the ones under SRS.(4)The maximum likelihood estimators(MLEs)of parameters in the PowerLindley distribution under minimum ranked set sampling with unequal samples was studied.The numerical results show that the MLEs under minimum ranked set sampling with unequal samples are significantly more efficient than the ones under SRS.