A Quantile Approach to the Interval Shannon Entropy

In this paper, we introduce and study quantile version of the Shannon entropy function via doubly truncated (interval) lifetime, which includes the residual and past lifetimes as special case. We aim to study the use of proposed measure in characterization of distribution functions. Further, we describe a stochastic order and a weighted distribution based on this entropy and show their properties. Finally, some results have been obtained for some distributions such as Uniform, Exponential, Pareto I, Power function and Govindarajulu. Also by analysing a real data the subject has been illustrated.