  In this work, we study the properties of cumulative residual entropy
generating function. We then introduce dynamic cumulative residual entropy
generating function (DCREGF). It is shown that the DCREGF determines the
distribution uniquely. We study some characterization results using the
relationship between DCREGF and hazard rate and mean residual life function. A
new class of life distribution based on decreasing DCREGF is introduced.
Finally we develop a test for decreasing DCREGF and study its performance.
