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Cumulative Tsallis entropy for maximum ranked set sampling with unequal samples

Author

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  • Tahmasebi, S.
  • Longobardi, M.
  • Kazemi, M.R.
  • Alizadeh, M.

Abstract

In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a non-additive generalization of Shannon entropy. We obtain several results of Tsallis entropy including bounds, monotonic properties, stochastic orders, and sharp bounds under some assumptions. We also compare the uncertainty and information content of MRSSU with its counterpart in the simple random sampling (SRS) data. Finally, we develop some characterization results in terms of cumulative Tsallis entropy and residual Tsallis entropy of MRSSU and SRS data.

Suggested Citation

  • Tahmasebi, S. & Longobardi, M. & Kazemi, M.R. & Alizadeh, M., 2020. "Cumulative Tsallis entropy for maximum ranked set sampling with unequal samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    • Handle: RePEc:eee:phsmap:v:556:y:2020:i:c:s037843712030385x
    DOI: 10.1016/j.physa.2020.124763
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    References listed on IDEAS

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    1. Calì, Camilla & Longobardi, Maria & Ahmadi, Jafar, 2017. "Some properties of cumulative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1012-1021.
    2. Wilk, G. & Włodarczyk, Z., 2008. "Example of a possible interpretation of Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4809-4813.
    3. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2018. "Measures of information for maximum ranked set sampling with unequal samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(19), pages 4692-4709, October.
    4. Thapliyal, Richa & Taneja, H.C. & Kumar, Vikas, 2015. "Characterization results based on non-additive entropy of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 297-303.
    5. Tahmasebi, Saeid & Jafari, Ali Akbar & Eskandarzadeh, Maryam, 2016. "Some results on residual entropy of ranked set samples," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 137-145.
    6. Kumar, Vikas & Rekha,, 2018. "A quantile approach of Tsallis entropy for order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 916-928.
    7. Tong, S. & Bezerianos, A. & Paul, J. & Zhu, Y. & Thakor, N., 2002. "Nonextensive entropy measure of EEG following brain injury from cardiac arrest," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 619-628.
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