A past inaccuracy measure based on the reversed relevation transform. (English) Zbl 1470.60068
Summary: 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.
MSC:
| 60E15 | Inequalities; stochastic orderings |
| 62B10 | Statistical aspects of information-theoretic topics |
| 62N05 | Reliability and life testing |
| 94A17 | Measures of information, entropy |
Keywords:
cumulative (past) entropy; mean inactivity time; reversed relevation transform; stochastic orders; proportional reversed hazard rates modelReferences:
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