Doubly truncated (interval) quantile Shannon entropy

It is well known that Shannon s entropy plays an important role in the measurement of uncertainty of probability distributions. Also, in statistical modelling and analysis of data there is an equivalent and alternate approach, through the quantile function (QF), which is very important in exploratory data analysis and in many other areas of applied statistics. In the present paper, we introduce and study quantile version of the Shannon entropy functions in doubly truncated (interval) lifetime, which includes the residual and past lifetimes as special case.