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

The complete cumulative residual entropy canbe generalizedto 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.