A new Kolmogorov-Smirnov test based on representative points in the exponential distribution family

Abstract

Hypothesis testing for the exponential distribution family consistently gains significant attentions from the statistical community, especially in situations characterized by small sample sizes. In this paper, we propose a novel approach for constructing a Kolmogorov-Smirnov type test based on representative points. This testing statistic is derived through a comparison between two empirical functions: one from the observed data and another from chosen representative points. A distribution-free quantile estimator is used for sample standardization. We also discuss how to select an optimal number of representative points based on the loss function, which is recommended for constructing the empirical function from the exponential distribution family. To evaluate the efficiency of this new test, a comprehensive Monte Carlo simulation is conducted to compare this new test with tailor-made tests. Simulation results show that our test statistic will be more powerful especially for small sample sizes, and it is competitive in the comparison with tailor-made tests. Some datasets are analyzed to further illustrate the efficiency of the proposed method.

Keywords:

• Representative points
• kolmogorov-smirnov type test
• the exponential distribution family
• the harrel-davis quantile estimator
• hypothesis testing

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was partially supported by the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College (2022B1212010006), and in part by Guangdong Higher Education Enhancement Plan [2021–2025] UIC (UICR0400011-22) and BNU-HKBU United International College internal research grant (R202010).