Estimating the Parameters of Truncated Gutenberg–Richter Distribution

—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 μ n . 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 Q T ( 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.