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Characterizations based on length-biased weighted measure of inaccuracy for truncated random variables. (English) Zbl 1340.60013
The notion of weighted residual inaccuracy measure was recently introduced by V. Kumar et al. [Metron 68, No. 2, 153–160 (2010; Zbl 1301.62104)] as an extension of the weighted measure of inaccuracy. These concepts derive from the classical Kerridge inaccuracy measure and are connected with the well-known Shannon’s entropy and Kullback-Leibler divergence.
The author studies the weighted residual inaccuracy measure under monotonic transformations and provides characterization theorems for some continuous distributions (uniform distribution, power distribution, exponential distribution, Weibull distribution, Rayleigh distribution and Pareto distributions) under the proportional (or the proportional reversed) hazard rate model. A similar study is made to the concept of weighted past inaccuracy measure introduced by V. Kumar and H. C. Taneja [Metrika 75, No. 1, 73–84 (2012; Zbl 1241.62014)].
A final comment (conclusion) reveals the applicability of the results.

60E15 Inequalities; stochastic orderings
62N05 Reliability and life testing
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