Parametric ranked set sampling

Ranked set sampling was introduced by McIntyre (1952,Australian Journal of Agricultural Research,3, 385–390) as a cost-effective method of selecting data if observations are much more cheaply ranked than measured. He proposed its use for estimating the population mean when the distribution of the data was unknown. In this paper, we examine the advantage, if any, that this method of sampling has if the distribution is known, for a specific family of distributions. Specifically, we consider estimation of and for the family of random variables with cdf's of the formF(x–/). We find that the ranked set sample does provide more information about both and than a random sample of the same number of observations. We examine both maximum likelihood and best linear unbiased estimation of and , as well as methods for modifying the ranked set sampling procedure to provide even better estimation.This paper has been prepared with partial support from the United States Environmental Protection Agency under Cooperative Agreement Number CR821801-01-0. The contents have not been subjected to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.