Dual-rank ranked set sampling

Abstract

In this paper, we propose a new sampling design extending the well-known ranked set sampling, which we named dual-rank ranked set sampling. Unlike the original ranked set sampling scheme, dual-rank ranked set sampling is based on two ranking sets stages, as the double ranked set sampling design. Dual-rank ranked set sampling differs from double ranked set sampling, however, since it requires only n 2 initially selected units to draw a sample of size n, whereas double ranked set sampling is based on n 3 units to provide a sample of similar size. We verified that the dual-rank ranked set sampling sample estimator of the population mean is an unbiased estimator for the corresponding population parameter when the underlying distribution is symmetric. A simulation study was carried out to evaluate the efficiency of dual-rank ranked set sampling. The simulation results pointed out that dual-rank ranked set sampling estimation is more efficient than simple random sampling and ranked set sampling, and it is a cost-effective alternative to double ranked set sampling estimation. The problem of interval estimation for dual-rank ranked set sampling was also addressed. An application based on fish ageing data is finally presented.