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A past inaccuracy measure based on the reversed relevation transform

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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.

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084, Fisciano, SA, Italy

    Antonio Di Crescenzo

  2. Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

    Suchandan Kayal

  3. Faculty of Basic Sciences and Engineering, Department of Mathematics and Statistics, Gonbad Kavous University, Gonbad Kavous, Iran

    Abdolsaeed Toomaj

Authors
  1. Antonio Di Crescenzo
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  2. Suchandan Kayal
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  3. Abdolsaeed Toomaj
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Correspondence to Antonio Di Crescenzo.

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Di Crescenzo, A., Kayal, S. & Toomaj, A. A past inaccuracy measure based on the reversed relevation transform. Metrika 82, 607–631 (2019). https://doi.org/10.1007/s00184-018-0696-6

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