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In this paper, we have developed conditions under which the entropy function and the residual entropy function characterize the distribution. We have also studied some stochastic comparisons based on the entropy measure and established relations between entropy comparisons and comparisons with respect to other measures in reliability. Conditions for decreasing (increasing) uncertainty in a residual life distribution are obtained. Some relations between the classes of distribution in reliability and the classes of distribution, based on the monotonic properties of uncertainty, in a residual life distribution are obtained.

Entropy and Residual Entropy Functions and Some Characterization Results