Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions

Fan Zhang; Zhiming Li

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arXiv · 2512.02832

Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions

Fan Zhang·Zhiming Li

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Abstract

Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an uncertain family-wise error rate is defined to control the overall error in simultaneous testing. Subsequently, a hypothesis test of two uncertain populations is proposed, and the rejection region for the null hypothesis at a significance level is derived, laying the foundation for further analysis. Building on this, a homogeneity test for multiple populations is developed to assess whether the unknown population parameters differ significantly. When there is no significant difference in these parameters among finite populations or within a subset, a common test is used to determine whether they equal a fixed constant. Finally, homogeneity and common tests for normal uncertain populations with means and standard deviations are conducted under three cases: only means, only standard deviations, or both are unknown. Numerical simulations demonstrate the feasibility and accuracy of the proposed methods, and a real example is provided to illustrate their effectiveness.

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Fan Zhang, Zhiming Li. 2025-12-02. Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions. https://arxiv.org/abs/2512.02832

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