Abstract: Uncertainty is closely related to amount of information and has been extensively studied in a variety of scientific fields including communication theory, probability theory and statistics. Given the information that the outcome of a random variable is in an interval, the uncertainty is expected to reduce when the interval shrinks. However, this conclusion is not always true. In this paper, we present the conditions under which the conditional extropy/cumulative residual entropy is a partially monotonic function of interval. Similar result is obtained for extropy of convolution of two independent and identically distributed random variables if their probability density functions are log-concave.

Key words: cumulative residual entropy, entropy, extropy, log-concavity, partially monotonicity