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To test the relationships of stochastic dominance, this paper firstly proposes two new consistent K-S-type statistics based on a quantile rule. Then, we consider their asymptotic properties. We introduce the bootstrap method to calculate the p-values of our proposed tests and use the Monte Carlo method to compare the power of our proposed test with the DD test and the BD test. The simulations showed that our test performed better than these two tests. Finally, we applied our proposed tests to compare the visibility of four provinces in China and compared the effects with the DD test and BD test. The empirical results showed that the conclusions of our proposed method are more-consistent with the dominance relationships of the four provinces. For a given significance level, the results of our proposed test demonstrate that the visibility of Jiangxi province is the best. The next one is the visibility of Hubei province, which outperforms the visibility of Anhui province. The visibility of Hunan province is the poorest. [ABSTRACT FROM AUTHOR]