Some extensions of Kullback-Leibler information based on survival function

In this article, we first investigate some extensions of Kullback-Leibler information and theirproperties. Then, we consider the moment constraints for the maximum distribution of cumulative residualentropy and investigate the relationship between the cumulative residual Kullback-Leibler information(CRKL) and cumulative residual entropy (CRE). We also discuss the methods for estimating the scaleparameter of Rayleigh distribution and provide two estimation methods. In the following we use cumulativeresidual Kullback-Leibler information as a goodness of fit test statistic. Then we compute the criticalvalues and the power of proposed tests and compare the power values with with the power of other tests.Finally, we apply the tests for a real data set.