Application of generalized extreme value distribution based on profile likelihood estimation in long term earthquake prediction

To describe the uncertainty of strong earthquake prediction, we introduced the profile likelihood estimation into parameter estimation of extreme value model for earthquake prediction. It is elaborated that the profile likelihood estimation principle and numerical algorithm of shape parameters and earthquake return level in generalized extreme value distribution. Meanwhile, a model of generalized extreme value distribution was created and was used to analyze the seismic risk of the East Kunlun seismic belt. The results showed that profile likelihood estimation and maximum likelihood estimation generated basically the same effect in point estimation of shape parameters and return level as well as the estimation of confidence interval of earthquake return level within 10 years. However, in the confidence interval estimation of moderate and long interval earthquake return level, the asymmetric confidence interval of return level obtained through the profile likelihood estimation can more accurately express the uncertainty of predicted magnitude of a strong earthquake and more effectively predict the outcome.