A past inaccuracy measure based on the reversed relevation transform

Antonio Di Crescenzo (), Suchandan Kayal () and Abdolsaeed Toomaj ()
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Antonio Di Crescenzo: Università degli Studi di Salerno
Suchandan Kayal: National Institute of Technology Rourkela
Abdolsaeed Toomaj: Gonbad Kavous University

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 5, No 5, 607-631

Abstract: 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; 60E15; 62B10; 62N05; 94A17 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-018-0696-6

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