Information Measures for Record Ranked Set Samples

Saeid Tahmasebi, Mahmoud Afshari, Maryam Eskandarzadeh

Abstract


Salehi and Ahmadi (2014) introduced a new sampling scheme for generating record-breaking data called record ranked set sampling. In this paper, we consider the uncertainty and information content of record ranked set samples (RRSS) in terms of Shannon entropy, Rényi and Kullback-Leibler (KL) information measures. We show that the difference between the Shannon entropy of RRSS and the simple random samples (SRS) is depends on the parent distribution F. We also compare the information content of RRSS with a SRS data in the uniform, exponential, Weibull, Pareto, and gamma distributions. We obtain similar results for RRSS under the Rényi information. Finally, we show that the KL information between the distribution of SRS and distribution of RRSS is distribution-free and increases as the sample size increases.

Keywords


Kullback-Leibler information. Record ranked set sampling design. Rényi information. Shannon entropy.

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DOI: https://doi.org/10.5902/2179460X19527

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