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A past inaccuracy measure based on the reversed relevation transform

Author

Listed:
  • Antonio Di Crescenzo

    (Università degli Studi di Salerno)

  • Suchandan Kayal

    (National Institute of Technology Rourkela)

  • Abdolsaeed Toomaj

    (Gonbad Kavous University)

Abstract

Numerous information indices have been developed in the information theoretic literature and extensively used in various disciplines. One of the relevant developments in this area is the Kerridge inaccuracy measure. Recently, a new measure of inaccuracy was introduced and studied by using the concept of relevation transform, which is related to the upper record values of a sequence of independent and identically distributed random variables. Along this line of research, we introduce an analogue of the inaccuracy measure based on the reversed relevation transform. We discuss some theoretical merits of the proposed measure and provide several results involving equivalent formulas, bounds, monotonicity and stochastic orderings. Our results are also based on the mean inactivity time and the new concept of reversed relevation inaccuracy ratio.

Suggested Citation

  • Antonio Di Crescenzo & Suchandan Kayal & Abdolsaeed Toomaj, 2019. "A past inaccuracy measure based on the reversed relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(5), pages 607-631, July.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:5:d:10.1007_s00184-018-0696-6
    DOI: 10.1007/s00184-018-0696-6
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    References listed on IDEAS

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    1. Vikas Kumar & H. Taneja & R. Srivastava, 2011. "A dynamic measure of inaccuracy between two past lifetime distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 1-10, July.
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    3. Nader Ebrahimi & Ehsan S. Soofi & Refik Soyer, 2010. "Information Measures in Perspective," International Statistical Review, International Statistical Institute, vol. 78(3), pages 383-412, December.
    4. Suchandan Kayal & Sunoj S. Madhavan & Rajesh Ganapathy, 2017. "On Dynamic Generalized Measures of Inaccuracy," Statistica, Department of Statistics, University of Bologna, vol. 77(2), pages 133-148.
    5. Jorge Navarro & Georgios Psarrakos, 2017. "Characterizations based on generalized cumulative residual entropy functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1247-1260, February.
    6. Suchandan Kayal, 2018. "On Weighted Generalized Cumulative Residual Entropy of Order n," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 487-503, June.
    7. Majid Rezaei & Behzad Gholizadeh & Salman Izadkhah, 2015. "On Relative Reversed Hazard Rate Order," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(2), pages 300-308, January.
    8. Georgios Psarrakos & Antonio Di Crescenzo, 2018. "A residual inaccuracy measure based on the relevation transform," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 37-59, January.
    9. Prem Nath, 1968. "Inaccuracy and coding theory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 13(1), pages 123-135, December.
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    Cited by:

    1. Jafar Ahmadi, 2021. "Characterization of continuous symmetric distributions using information measures of records," Statistical Papers, Springer, vol. 62(6), pages 2603-2626, December.

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