نمونه‌گيري مجموعه رتبه‌دار دوگان‌رتبه

selec‎ting an appropriate sampling method is one of the fundamental an‎d decisive issues in statistical research. Researchers have continually sought efficient sampling designs that, considering the nature of the data, can provide more accurate an‎d reliable estimates of population parameters while reducing implementation costs. In this context, Ranked Set Sampling (RSS) has attracted considerable attention as an efficient alternative to Simple Ran‎dom Sampling, particularly in situations where ranking sampling units can be performed at a relatively low cost. The primary objective of this thesis is to introduce an‎d investigate the properties of a generalized ranked-set-based sampling design, referred to as «Dual-rank Ranked Set Sampling» (DRRSS), along with several other rank-based sampling schemes, including Ranked Set Sampling, Neoteric Ranked Set Sampling (NRSS), an‎d Double-ranked Set Sampling (DRSS), for estimating the population mean. The performance of the considered sampling schemes is eva‎luated using measures such as bias, relative efficiency, percentile bootstrap confidence interval length, an‎d coverage probability. In this thesis, the behavior of rank-based sampling schemes under symmetric, asymmetric, an‎d discrete distributions is studied through Monte Carlo simulation an‎d bootstrap methods under both perfect an‎d imperfect ranking conditions. The simulation results indicate that the superiority of the sampling schemes depends on the study conditions, an‎d each design performs more effectively in certain situations. The performance of these schemes is influenced by factors such as the type of population distribution, ranking quality, set size, an‎d the number of cycles. In general, the NRSS an‎d DRRSS schemes, by making more effective use of ranking information, tend to produce shorter confidence intervals in many cases, whereas the RSS an‎d DRSS schemes demonstrate more reliable behavior in terms of coverage probability. Furthermore, the findings reveal that ranking quality plays a crucial role in the efficiency of rank-based sampling schemes, an‎d increasing the number of cycles improves their coverage probability. These results suggest that selec‎ting an appropriate sampling design should be carried out according to the objectives of the study an‎d the characteristics of the data.

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