, Volume 82, Issue 1, pp 17–38 | Cite as

Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime

  • Aswathy S. Krishnan
  • S. M. SunojEmail author
  • P. G. Sankaran


Measure of uncertainty in past lifetime plays an important role in different areas such as information theory, reliability theory, survival analysis, economics, business, forensic science and other related fields. In this paper, we propose a cumulative Tsallis entropy in past lifetime based on quantile function. We obtain different characterizations based on the proposed measure and quantile-based reliability measures. We also study the quantile-based cumulative Tsallis entropy of order statistics in past lifetime.


Order statistics Quantile function Incomplete beta Past entropy Reversed Hazard quantile function Mean inactivity time 

Mathematics Subject Classification

94A17 62N05 



First author is thankful to the Kerala State Council for Science, Technology and Environment (KSCSTE), India (Order No: 1127/2017/KSCSTE/Thiruvananthapuram) for the financial support. The second and third authors would like to thank the support of the University Grants Commission, India, under the Special Assistance Programme.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Aswathy S. Krishnan
    • 1
  • S. M. Sunoj
    • 1
    Email author
  • P. G. Sankaran
    • 1
  1. 1.Department of StatisticsCochin University of Science and TechnologyCochinIndia

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