ABSTRACT
In the same manner as Shannon entropy was generalized to give alternative measures, there have been similar attempts on cumulative entropy that gave several new measures of uncertainty. In Section 2 we provide the results on survival and failure entropies. That includes characterizations, orderings, weighted versions etc. In Section 3 we have the cumulative divergence extending the K-L divergence. Following this the next section contains results on cumulative Tsallis entropy. A discussion on the weighted form with special results is an interesting aspect with applications and the quantile version are some of the topics in the subsequent sections. Section 6 is on cumulative residual inaccuracy and the next section describes generalization of cumulative entropies in different directions. These discussions related to relevation transforms have potential applications in replacement strategies, actuarial science and other related areas.
