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

TL;DR

This paper develops hypothesis testing methods for multiple uncertain finite populations, extending existing approaches to broader scenarios with applications to normal uncertainty distributions, supported by simulations and real data.

Contribution

It introduces new hypothesis tests for multiple uncertain populations, including homogeneity and common tests, with a focus on normal uncertainty distributions, expanding the scope of uncertain statistics.

Findings

Proposed tests effectively control error rates in multiple uncertain populations.

Numerical simulations confirm the accuracy and feasibility of the methods.

Real data example demonstrates practical applicability.

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.