Ranked set sample design for environmental investigations

Ranked set sampling can provide an efficient basis for estimating parameters of environmental variables, particularly when sampling costs are intrinsically high. Various ranked set estimators are considered for the population mean and contrasted in terms of their efficiencies and useful- ness, with special concern for sample design considerations. Specifically, we consider the effects of the form of the underlying random variable, optimisation of efficiency and how to allocate sampling effort for best effect (e.g. one large sample or several smaller ones of the same total size). The various prospects are explored for two important positively skew random variables (lognormal and extreme value) and explicit results are given for these cases. Whilst it turns out that the best approach is to use the largest possible single sample and the optimal ranked set best linear estimator (ranked set BLUE), we find some interesting qualitatively different conclusions for the two skew distributions