To overcome the drawbacks of Shannon's entropy, the concept of cumulative residual and past entropy has been proposed in the information theoretic literature. Furthermore, the Shannon entropy has been generalized in a number of different ways by many researchers. One important extension is Kerridge inaccuracy measure. In the present communication we study the cumulative residual and past inaccuracy measures, which are extensions of the corresponding cumulative entropies. Several properties, including monotonicity and bounds, are obtained for left, right and doubly truncated random variables

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Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability theory to characterize some wellknown distributions. However, there has been growing interest in the study of these functions in reversed time and their applications. In the present work we consider reversed hazard rate, expected inactivity time and reversed aging intensity function to deal with right truncated random variables and characterize a few statistical distributions.