A past inaccuracy measure based on the reversed relevation transform
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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.
KeywordsCumulative (past) entropy Mean inactivity time Reversed relevation transform Stochastic orders Proportional reversed hazard rates model
Mathematics Subject Classification60E15 62B10 62N05 94A17
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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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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