A past inaccuracy measure based on the reversed relevation transform

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.

A measure of inaccuracy in concomitants of ordered random variables under Farlie-Gumbel-Morgenstern family

“…Thapliyal and Taneja [26] have proposed the measure of residual inaccuracy of order statistics and prove a characterization result for it. For a further view of the literature survey on inaccuracy measure see Kundu and Nanda [19], Kayal et al [14], Psarrakos and Di Crescenzo [22], Kayal et al [16], Kayal and Sunoj [15] and Di Crescenzo et al [4]. The rest of this dissertation is organized as follows: Section 2 derives the inaccuracy and its dynamic residual of the distribution of the rth concomitants of os and f (y) and vice versa.…”