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.

翻译：关于熵的生成函数方法的研究逐渐流行，因其能够生成文献中讨论的多种著名熵度量。本文定义了加权累积残差熵生成函数（WCREGF）并研究其性质，进而引入动态加权累积残差熵生成函数（DWCREGF）。研究表明，DWCREGF能唯一确定分布。我们利用DWCREGF与风险率及/或平均剩余寿命函数之间的关系，讨论了一些表征结果。基于DWCREGF的表征，我们针对瑞利分布提出了一种新的拟合优度检验方法。通过蒙特卡洛模拟研究评估了所提出的检验，最后利用两个真实数据集对该检验进行了说明。