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Statistical Papers

, Volume 60, Issue 3, pp 933–943 | Cite as

Some properties of cumulative Tsallis entropy of order \(\alpha \)

  • G. Rajesh
  • S. M. SunojEmail author
Regular Article

Abstract

Tsallis entropy of order \(\alpha \) (see Tsallis in J Stat Phys 52(1–2):479–487, 1988) plays an important role in the measurement uncertainty of random variables. Recently, Sati and Gupta (J Probab Stat, doi: 10.1155/2015/694203, 2015) introduced a cumulative Tsallis entropy of order \(\alpha \) and studied its various properties in the context of reliability modeling. In this paper, we introduce an alternate measure of cumulative Tsallis entropy of order \(\alpha \) and study its properties. Unlike the cumulative Tsallis entropy due to Sati and Gupta (J Probab Stat, doi: 10.1155/2015/694203, 2015), the proposed measure has some additional features and has simple relationships with other important information and reliability measures.

Keywords

Tsallis entropy Cumulative residual entropy Reliability measures 

Mathematics Subject Classification

94A17 62N05 

Notes

Acknowledgements

The authors wish to thank the support of University Grants Commission, India, under Special Assistance Programme. The authors wish to thank the editor and referees for their constructive comments.

References

  1. Abbasnejad M, Arghami NR, Morgenthaler S, Mohtashami Borzadaran GR (2010) On the dynamic survival entropy. Stat Probab Lett 80:1962–1971MathSciNetCrossRefzbMATHGoogle Scholar
  2. Asadi M, Zohrevand Y (2007) On the dynamic cumulative entropy. J Stat Plan Inference 137:1931–1941MathSciNetCrossRefzbMATHGoogle Scholar
  3. Baratpour S (2010) Characterizations based on cumulative residual entropy of first orderstatistics. Commun Stat 39:3645–3651MathSciNetCrossRefzbMATHGoogle Scholar
  4. Cartwright J (2014) Roll over. Boltzmann. Phys World 27(5):31–35CrossRefGoogle Scholar
  5. Di Crescenzo A, Longobardi M (2009) On cumulative entropies. J Stat Plan Inference 139:4072–4087MathSciNetCrossRefzbMATHGoogle Scholar
  6. Ebrahimi N, Pellerey F (1995) Partial ordering of survival functions based on the notion of uncertainty. J Appl Probab 32:202–211MathSciNetCrossRefzbMATHGoogle Scholar
  7. Navarro J, del Aguila Y, Asadi M (2010) Some new results on the cumulative residual entropy. J Stat Plan Inference 140:310–322MathSciNetCrossRefzbMATHGoogle Scholar
  8. Rao M, Chen Y, Vemuri BC, Wang F (2004) Cumulative residual entropy: a new measure of information. IEEE Trans Inf Theory 50(6):1220–1228MathSciNetCrossRefzbMATHGoogle Scholar
  9. Sati MM, Gupta N (2015) Some characterization results on dynamic cumulative residual Tsallis entropy. J Probab Stat. doi: 10.1155/2015/694203
  10. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetCrossRefzbMATHGoogle Scholar
  11. Sunoj SM, Linu MN (2012) Dynamic cumulative residual Renyi entropy. Statistics 46:1–56MathSciNetCrossRefzbMATHGoogle Scholar
  12. Tsallis C (1988) Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 52(1–2):479–487MathSciNetCrossRefzbMATHGoogle Scholar
  13. Zardasht V, Parsi S, Mousazadeh M (2015) On empirical cumulative residual entropy and a goodness-of-fit test for exponentiality. Stat Pap 56:677–688MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of StatisticsCochin University of Science and TechnologyCochinIndia

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