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Estimation of the upper cutoff parameter for the tapered Pareto distribution

Part of: Parametric inference

Published online by Cambridge University Press:  14 July 2016

Y. Y. Kagan  and
F. Schoenberg
Y. Y. Kagan*
Affiliation:
University of California
F. Schoenberg*
Affiliation:
University of California
*
1Postal address: Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095–1567, USA. Email: [email protected]
2Postal address: Department of Statistics, University of California, Los Angeles, CA 90095–1554, USA. Email: [email protected]
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Abstract

The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.

Keywords

Parameter estimationtapered Pareto distributionGutenberg-Richter relationmaximum likelihood estimationmethod of momentsearthquakes

MSC classification

Primary: 62F10: Point estimation
Secondary: 62F12: Asymptotic properties of estimators 62F25: Tolerance and confidence regions 62F15: Bayesian inference
Type
Models and statistics in seismology
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 158 - 175
Copyright
Copyright © Applied Probability Trust 2001 

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