2013/01/18 by Mohammad Jafari Jozani, Jozani, Mohammad Jafari, Jafar Ahmadi +1 · 1 citation
Mathematics · #62B10 #62D05 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy Systems and Optimization #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #msc:62B10 #msc:62D05 #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1301.4292
15 pages, 2 figures
arxiv created 2013/01/18 · openalex publication_date 2013/01/18 · arxiv updated 2013/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Ranked set sampling is a sampling design which has a wide range of applications in industrial statistics, and environmental and ecological studies, etc.. It is well known that ranked set samples provide more Fisher information than simple random samples of the same size about the unknown parameters of the underlying distribution in parametric inferences. In this paper, we consider the uncertainty and information content of ranked set samples in both perfect and imperfect ranking scenarios in terms of Shannon entropy, Rényi and Kullback-Leibler (KL) information measures. It is proved that under these information measures, ranked set sampling design performs better than its simple random sampling counterpart of the same size. The information content is also a monotone function of the set size in ranked set sampling. Moreover, the effect of ranking error on the information content of the data is investigated.