In this article, the maximum likelihood estimators (MLEs) of the scale and shape parameters β and λ from the Exponential-Poisson distribution will be considered in moving extremes ranked set sampling (MERSS). These MLEs will be compared in terms of asymptotic efficiencies. The numerical results show that the MLEs obtained via MERSS can serve as effective alternatives to those derived from simple random sampling.

The existence and uniqueness of the maximum likelihood estimator (MLE) of parameter for the exponential-Poisson distribution is discussed by Kuş [2007. A new lifetime distribution. Computational Statistics and Data Analysis 51(9): 4497–4509] in simple random sampling (SRS). As an alternative to the MLEs in SRS, Joukar et al. [2021. Parameter estimation for the exponential-poisson distribution based on ranked set samples. Communication in Statistics-Theory and Methods 50(3): 560–581] discussed the MLE of parameter for this distribution in ranked set sampling (RSS). However, they did not discuss the existence and uniqueness of the MLE in RSS and did not provide explicit expressions for the Fisher information in RSS. In this article, we discuss the existence and uniqueness of the MLE of parameter in RSS and give explicit expressions for the Fisher information in RSS. The MLEs will be compared in terms of asymptotic efficiencies. Numerical studies and a real data application show that these MLEs in RSS can be real competitors for those in SRS.

The traditional simple random sampling (SRS) design method is ine cient in many cases. Statisticians proposed some new designs to increase e ciency. In this paper, as a variation of moving extremes ranked set sampling (MERSS), double MERSS (DMERSS) is proposed and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DMERSS gives unbiased estimators of the population mean. Also, it is found that DMERSS is more e cient than the SRS and MERSS methods for usual symmetric distributions (normal and uniform). For asymmetric distributions considered in this study, the DMERSS has a small bias and it is more e cient than SRS for usual asymmetric distribution (exponential) for small sample sizes.

Maximum ranked set sampling with unequal samples is a sampling procedure used to reduce the error of ranking of observations and increase the efficiency of statistical inference. It is used for maximum likelihood estimation of the location and shape parameters of the inverse Gaussian distribution. Its asymptotic efficiency is at least 1.4 times higher than those of estimators based on simple random sampling. It is useful in reliability studies and in Bayesian statistics involving the inverse Gaussian distribution.

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 λ and α 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 λ and α from GR distribution in SRS and RSS are studied. The numerical results show that the modified unbiased estimator and the modified BLUE of λ and α in RSS are significantly more efficient than the ones in SRS.