Quantile-Based Cumulative Information Generating Functions

In this communication, quantile-based cumulative information generating functions with some of its properties have been addressed. It is shown that the quantile-based cumulative past and residual entropy generating functions can be deduced from this general quantile-based measure for particular values of the parameters. Quantile-based dynamic cumulative past information generating function and quantile-based dynamic cumulative residual information generating function have been studied. Relations between the proposed measures with some reliability measures have been proposed. Characterization results for the power and exponential distributions have been obtained. Quantile-based stochastic ordering results are also derived.