Information Sciences, ( ISI ), Volume (264), No (1), Year (2014-3) , Pages (291-301)

Title : ( On uncertainty and information properties of ranked set samples )

Authors: Mohammad Jafari Jozani , Jafar Ahmadi ,

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Abstract

‎Ranked set sampling is a sampling design which has a wide range of applications in industrial statistics‎, ‎economics 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, ‎Renyi 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.

Keywords

, Ranked set sampling; Kullback, Leibler; Order statistics; Imperfect ranking; Renyi Information; Shannon entropy‎.