Bias, variance and computational properties of Kijko's estimators of the upper limit of magnitude distribution, Mmax

It is often assumed in probabilistic seismic hazard analysis that the magnitude distribution has an upper limit M (max), which indicates a limitation on event size in specific seismogeneic conditions. Accurate estimation of M (max) from an earthquake catalog is a matter of utmost importance. We compare bias, dispersion and computational properties of four popular M (max) estimators, introduced by Kijko and others (e.g., Kijko and Sellevoll 1989, Kijko and Graham 1998, Kijko 2004) and we recommend the ones which can be the most fruitful in practical applications. We provide nomograms for evaluation of bias and standard deviation of the recommended estimators for combinations of sample sizes and distribution parameters. We suggest to use the bias nomograms to correct the M (max) estimates. The nomograms of standard deviation can be used to determine minimum sample size for a required accuracy of M (max).