Generalized fiducial inference for the GEV change-point model

Abstract

Generalized extreme value (GEV) distribution is used to analyse the maximum from a block of data. It is very useful to describe the unusual event rather than the usual event. In this paper, we propose a change-point detection procedure for GEV distribution based on generalized fiducial inference. The fiducial distribution of the change-point location is constructed. Meanwhile, Markov Chain Monte Carlo method combined with Gibbs sampling and the Metropolis–Hastings algorithm is utilised to estimate the location of the change point and its confidence interval. In addition, the generalized fiducial factor is used to test whether there is a change point. Simulation results show that the proposed generalized fiducial method performs better in accuracy, robustness and the length of confidence intervals. Finally, we apply the proposed method to the annual maximum rainfall data in Beijing.

Keywords:

• Generalized fiducial inference
• GEV distribution
• MCMC
• change point

Disclosure statement

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

Additional information

Funding

This work was supported by the Natural Science Foundation of Hebei Province [grant number A2022208001]; the National Natural Science Foundation of China [grant number 12001155].