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Metrika

, Volume 82, Issue 5, pp 607–631 | Cite as

A past inaccuracy measure based on the reversed relevation transform

  • Antonio Di CrescenzoEmail author
  • Suchandan Kayal
  • Abdolsaeed Toomaj
Article

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.

Keywords

Cumulative (past) entropy Mean inactivity time Reversed relevation transform Stochastic orders Proportional reversed hazard rates model 

Mathematics Subject Classification

60E15 62B10 62N05 94A17 

Notes

Acknowledgements

The first author is a member of the Research group GNCS of INdAM. The third author is partially supported by a grant from Gonbad Kavous University.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

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

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di SalernoFiscianoItaly
  2. 2.Department of MathematicsNational Institute of Technology RourkelaRourkelaIndia
  3. 3.Faculty of Basic Sciences and Engineering, Department of Mathematics and StatisticsGonbad Kavous UniversityGonbad KavousIran

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