eprintid: 1282 rev_number: 21 eprint_status: archive userid: 2 dir: disk0/00/00/12/82 datestamp: 2015-02-17 11:36:37 lastmod: 2018-03-28 09:53:36 status_changed: 2015-04-27 12:10:36 type: article metadata_visibility: show creators_name: Lasocki, Stanislaw creators_name: Urban, Pawel creators_id: lasocki@igf.edu.pl creators_id: urban@igf.edu.pl corp_creators: Institute of Geophysics, Polish Academy of Sciences, Warszawa, Poland title: Bias, variance and computational properties of Kijko’s estimators of the upper limit of magnitude distribution, Mmax ispublished: pub subjects: MP2_2 subjects: MP3_1 subjects: MP5 divisions: EPOS-P full_text_status: none keywords: M max estimation, M max bias, M max variance, magnitude distribution, seismic hazard abstract: 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. date: 2011-08 date_type: published publication: Acta Geophysica volume: 59 number: 4 publisher: Versita, Warsaw and Springer-Verlag Berlin Heidelberg id_number: doi:10.2478/s11600-010-0049-y refereed: TRUE issn: 1895-6572 official_url: http://dx.doi.org/10.2478/s11600-010-0049-y access_IS-EPOS: limited software_references: Seismic_Hazard_Assessment owner: Publisher citation: Lasocki, Stanislaw and Urban, Pawel (2011) Bias, variance and computational properties of Kijko’s estimators of the upper limit of magnitude distribution, Mmax. Acta Geophysica, 59 (4). DOI: https://doi.org/10.2478/s11600-010-0049-y