A test for the increasing convex order based on the cumulative residual entropy

The complete cumulative residual entropy can be generalized to the incomplete cumulative residual entropy (ICRE). In this paper, we introduce a partial ordering in terms of ICRE. The relationship between this ordering and some important orderings of lifetime distributions are investigated. We use this order to establish a test statistic for testing the stochastic equality against increasing convex order alternative. The performance of the test statistic is evaluated using a simulation study. Finally, a numerical example illustrating the theory is also given.