TY - JOUR
T1 - A new Kolmogorov-Smirnov test based on representative points in Weibull distributions
AU - Wang, Sirao
AU - Liang, Jiajuan
AU - Peng, Heng
AU - Ye, Huajun
N1 - This work was partially supported by the Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science, BNU-HKBU United International College (UIC), project code 2022B1212010006 and UIC research grants R0400001-22.
Publisher Copyright:
© 2024 Taylor & Francis Group, LLC.
PY - 2024/9/4
Y1 - 2024/9/4
N2 - Hypothesis testing for the Weibull distribution always raises attention in the literature. It is challenging especially in small-sample scenarios. In this paper, we propose a new Kolmogorov-Smirnov type test based on the distance between two empirical functions, one from the data and another from the representative points of the underlying distribution. A bias correction technique is used to estimate unknown parameters in the Weibull distribution. We also discuss how to choose a suitable number of representative points based on the proposed loss function, which is recommended for constructing the empirical function from the Weibull distribution. To compare with tailor-made tests in the literature, a simulation study of the empirical type I error and testing power is conducted. It shows that our proposed test statistic is more powerful in most alternative scenarios, and it significantly improves the power of testing in small-sample scenarios. Finally, two real-world datasets are conducted to further demonstrate the efficiency of the proposed method.
AB - Hypothesis testing for the Weibull distribution always raises attention in the literature. It is challenging especially in small-sample scenarios. In this paper, we propose a new Kolmogorov-Smirnov type test based on the distance between two empirical functions, one from the data and another from the representative points of the underlying distribution. A bias correction technique is used to estimate unknown parameters in the Weibull distribution. We also discuss how to choose a suitable number of representative points based on the proposed loss function, which is recommended for constructing the empirical function from the Weibull distribution. To compare with tailor-made tests in the literature, a simulation study of the empirical type I error and testing power is conducted. It shows that our proposed test statistic is more powerful in most alternative scenarios, and it significantly improves the power of testing in small-sample scenarios. Finally, two real-world datasets are conducted to further demonstrate the efficiency of the proposed method.
KW - Representative points
KW - Kolmogorov-Smirnov test
KW - The Weibull distribution
KW - Hypothesis testing
KW - The power of testing
UR - http://www.scopus.com/inward/record.url?scp=85203068296&partnerID=8YFLogxK
U2 - 10.1080/03610918.2024.2391871
DO - 10.1080/03610918.2024.2391871
M3 - Journal article
AN - SCOPUS:85203068296
SN - 0361-0918
JO - Communications in Statistics: Simulation and Computation
JF - Communications in Statistics: Simulation and Computation
ER -