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Saddlepoint p-values for a class of location-scale tests
Abd El-Raheem M Abd El-Raheem1, Haidy N Mohamed1, Ehab F Abd-Elfattah1
1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt.
Abstract:
The main idea of this paper is to approximate the exact p-value of a class of non-parametric, two-sample location-scale tests. In this paper, the most famous non-parametric two-sample location-scale tests are formulated in a class of linear rank tests. The permutation distribution of this class is derived from a random allocation design. This allows us to approximate the exact p-value of the non-parametric two-sample location-scale tests of the considered class using the saddlepoint approximation method. The proposed method shows high accuracy in approximating the exact p-value compared to the normal approximation method. Moreover, the proposed method only requires a few calculations and time, as in the case of the simulated method. The procedures of the proposed method are clarified through four sets of real data that represent applications for a number of different fields. In addition, a simulation study compares the proposed method with the traditional methods to approximate the exact p-value of the specified class of the non-parametric two-sample location-scale tests.
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