Weighted cumulative residual entropy generating function and its use in testing Rayleigh distribution

The study of the generating function approach to entropy has gained popularity due to its ability to produce several well-known entropy measures found 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 uniquely determines the distribution. 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 propose a new goodness-of-fit test for the Rayleigh distribution. A Monte Carlo simulation study is conducted to evaluate the performance of the proposed test. Finally, the test is illustrated by means of two real data sets.