Estimation Of Location And Scale Parameter Of Symmetrical Distribution In The Two Stage Ranked Set Sampling

In the theory of statistical inference, simple random sampling (SRS) method is simple, easy to operate. With contrast, ranked set sampling (RSS) although need to sort, but with less sample volume can acquire more information. In the estimation of the parameters, using ranked set sampling samples is better than the simple random sampling sample. Based on ranked set sampling, derived from a variety of sampling methods, such as extreme ranked set sampling (ERSS), the median ranked set sampling (MRSS),balanced groups ranked set sampling(BGRSS). Based on balanced groups ranked set sampling, the reference [1] is proposed in the improved two stage ranked set sampling (TSBGRSS), and pointed out that in the location parameters of the symmetrical distribution estimation, this method is better than the other sampling methods, but this paper only gives an unbiased estimate. Based on the above consideration, when the overall distribution is symmetrical, this article follow the two stage balance ranked set sampling method, discusses the nature of the overall subject location scale parameter distributions of the order statistics of the expectation and variancein,and gives the best linear unbiased estimator of the location and scale parameters based on this sampling. Finally, this article gives the relative efficiency between the estimator of the location parameter which is given in reference [1] and the best linear unbiased estimator of the location parameter which is given in this article.