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Confidence intervals of b values for grouped magnitudes

UNIVERSITÀ DI BOLOGNA DIPARTIMENTO DI FISICA SETTORE DI GEOFISICA, VIALE BERTI PICHAT 8, 40127 BOLOGNA, Italy

Abstract

This paper presents a simple method, that is a very practical tool, to compute the confidence intervals of parameter b for earthquake magnitudes grouped in classes of equal width—a circumstance that happens quite frequently in the usual applications in seismology. The problem is given a solution which is complete and covers very satisfactorily all cases of concern for the seismologist. The authentic, innovative contribution of the paper is that, by exploiting the strict connection between the frequency-magnitude Gutenberg-Richter law and the discrete geometric distribution, an approach is followed that allows for the evaluation of the confidence bands even for samples with a small number of earthquakes (N < 40).

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