The Estimation Of Location-scale Distributions Under Ranked Set Sampling

When we do statistical inference work, compared ranked set sampling with simple random sampling, ranked set sampling can gain same information with the less samples or more information with the same samples,we derive estimators under ranked set sampling more efficient than the estimators under simple random sampling. Sometimes it is difficult for us to measure large order statistics accurately, the measure of small order statistic is easier than the measure of large order statistics. and in the symmetrical distribution,the small order statistic can reflect some information of large order statistics. So in the article,Considering that the population distribution obey symmetrical distribution. Firstly, a ranked set sampling method is distill the order of the double diagonal samples. In the article, we present a new sampling method, in which method, we distill the order of the left part of the main diagonal and the secondary diagonal sample.Secondly,In the condition of the total from location-scale parameter distributions,the article studies the expectation and variance of the order statistics.Thirdly,we present the best liner unbiased estimator of the location parameter and scale parameter of the symmetrical location-scale parameter distributions under the new methods of ranked set sampling.Proved that the Sibel Balci and Aysen D.Akkaya’s article,scale parameter’s the best liner unbiased estimator from paired sample equals scale parameter’s the best liner unbiased estimator In this paper. Fourth, we present the compared standard relative efficiency of location parameter’s the best liner unbiased estimator and scale parameter’s the best liner unbiased estimator,with main diagonal ranked set sampling method and new ranked set sampling method.