  The study on the generating function approach to entropy become popular as it
generates several well-known entropy measures discussed in the literature. In
this work, we define the weighted cumulative residual entropy generating
function (WCREGF) and study its properties. We then introduce the dynamic
weighted cumulative residual entropy generating function (DWCREGF). It is shown
that the DWCREGF determines the distribution uniquely. We study some
characterization results using the relationship between the DWCREGF and the
hazard rate and/or the mean residual life function. Using a characterization
based on DWCREGF, we develop a new goodness fit test for Rayleigh distribution.
A Monte Carlo simulation study is conducted to evaluate the proposed test.
Finally, the test is illustrated using two real data sets.
