In this paper, we study several incomplete entropy measures, namely the Incomplete Weighted Cumulative Residual Entropy, the Incomplete Cumulative Residual Tsallis Entropy and its weighted version, and introduce the associated partial orderings. Their connections with certain well-known stochastic orderings are also investigated. Based on these characterizations, a class of nonparametric tests for stochastic equality against ordered alternatives is developed. The asymptotic properties of the proposed tests are derived, while their finite-sample performances are assessed through extensive Monte Carlo simulations under various alternative models and sample sizes. These tests are further compared with the test based on incomplete cumulative residual entropy proposed by Zardasht (2015).
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