Por Tom Reynkens (Research Centre Insurance – Leuven - Belgium).
The area-characteristic, maximum possible earthquake magnitude is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg-Richter law predicts that earthquake magnitudes follow a truncated exponential distribution. In the geophysical literature several parametric and non-parametric estimation procedures were proposed. Estimation of the maximum possible earthquake magnitude is of course an extreme value problem to which the classical methods for endpoint estimation could be applied. We argue that recent methods on truncated tails at high levels (Beirlant et al., Extremes, 2016; Electron. J. Stat., 2017) constitute a more appropriate setting for this estimation problem. We present upper confidence bounds to quantify the uncertainty of the point estimates. We also compare methods from the extreme value and geophysical literature through simulations. Finally, the different methods are applied to the magnitude data for the earthquakes induced by gas extraction in the Groningen province of the Netherlands.
