Fisher information for generalized Rayleigh distribution in ranked set sampling design with application to parameter estimation

In the current paper, we considered the Fisher information matrix from the generalized Rayleigh distribution (GR) distribution in ranked set sampling (RSS). The numerical results show that the ranked set sample carries more information about lambda and alpha than a simple random sample of equivalent size. In order to give more insight into the performance of RSS with respect to (w.r.t.) simple random sampling (SRS), a modified unbiased estimator and a modified best linear unbiased estimator (BLUE) of scale and shape lambda and alpha from GR distribution in SRS and RSS are studied. The numerical results show that the modified unbiased estimator and the modified BLUE of lambda and alpha in RSS are significantly more efficient than the ones in SRS.