Quantile-based cumulative entropies

Abstract

ABSTRACTIt is well known that Shannon’s entropy plays an important role in the measurement of uncertainty of probability distributions. However, in certain situations Shannon entropy is not appropriate to measure the uncertainty and therefore an alternative measure has been introduced called cumulative residual entropy, based on the survival function (sf) instead of the probability density function (pdf) f(x) used in Shannon’s entropy. In the present paper, we introduce and study quantile versions of the cumulative entropy functions in the residual and past lifetimes. Unlike the cumulative entropies based on sf, the quantile-based cumulative entropy measures uniquely determine the underlying probability distribution.