Parameter estimation of probability distributions based on ranked set sampling

Recently, many researchers focused on the more effective sampling method that is called Ranked Set Sampling (RSS) for estimating the population parameter when the measurement of an observation is costly and/or time consuming. In RSS procedure, we rank the units of the variable of interest without actual measurement and after the ranking process, only selected units are measured exactly. Therefore, we have effectiveness and advantageous as time and cost. Furthermore, it provides more representative sample from the target population by selecting the units almost everywhere from the interested population. RSS method has been studied by the number of researchers under various scopes. While some of them has modified the RSS, the others estimated the parameter of population by using these modifications. In this study, we deal with the estimation of the shape and scale parameters for Generalized Rayleigh (GR) distribution. We propose the maximum likelihood (ML) estimators of unknown parameters of GR distribution based on RSS and its some modifications. As we have no explicit form of estimators of parameters, numerical methods are used for the solutions. For comparison of the performances of estimators, a Monte Carlo simulation study is performed via Mathematica 11.0 with 10,000 repetitions. The biases, mean squared errors and relative efficiencies of estimators are compared in simple random sampling (SRS), RSS, extreme RSS, median RSS and imperfect RSS with different set and cycle sizes. Moreover, the study is supported with a real data example.