A new Kolmogorov-Smirnov test based on representative points in Weibull distributions

Sirao Wang, Jiajuan Liang, Heng Peng, Huajun Ye*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)

Abstract

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.
Original languageEnglish
JournalCommunications in Statistics: Simulation and Computation
DOIs
Publication statusE-pub ahead of print - 4 Sept 2024

Scopus Subject Areas

  • Statistics and Probability
  • Modelling and Simulation

User-Defined Keywords

  • Representative points
  • Kolmogorov-Smirnov test
  • The Weibull distribution
  • Hypothesis testing
  • The power of testing

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