Estimating the Parameters of Truncated Gutenberg–Richter Distribution

Abstract

Abstract—In the framework of the truncated Gutenberg–Richter distribution model, the problem of estimating the maximum possible regional magnitude M is considered. A new estimator of parameter M is proposed based on the bias-corrected maximum likelihood estimate, for which an exact formula is derived in the form of a finite sum of some functions of sample maximum μn. The new estimate is compared with some known estimates of parameter M and its fairly high efficiency is shown. Using a similar technique, an estimate is obtained of quantile QT(q) of the maximum earthquake magnitude in a given future time interval T. It is shown that the distribution density of magnitudes is significantly distorted at the ends of the magnitude range when using the model of magnitude perturbation by random errors.