Confidence intervals of b values for grouped magnitudes

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

[1]  On estimating frequency-magnitude relations from heterogeneous catalogs , 1987 .

[2]  P. Guttorp,et al.  On estimating varying b values , 1986 .

[3]  Yosihiko Ogata,et al.  Unbiased Estimate for $b$-value of Magnitude Frequency(Non-Regular Statistical Estimation II) , 1986 .

[4]  F. Mulargia,et al.  Effects of magnitude uncertainties on estimating the parameters in the Gutenberg-Richter frequency-magnitude law , 1985 .

[5]  Bernice Bender,et al.  Maximum likelihood estimation of b values for magnitude grouped data , 1983 .

[6]  B. Bolt,et al.  The standard error of the magnitude-frequency b value , 1982 .

[7]  J. B. Berrill,et al.  Maximum entropy and the magnitude distribution , 1980 .

[8]  D. L. Anderson,et al.  Theoretical Basis of Some Empirical Relations in Seismology by Hiroo Kanamori And , 1975 .

[9]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[10]  T. Utsu.  A Statistical Significance Test of the Difference in b-value between Two Earthquake Groups , 1966 .

[11]  K. Aki.  17. Maximum Likelihood Estimate of b in the Formula logN=a-bM and its Confidence Limits , 1965 .

[12]  T. Utsu.  A method for determining the value of b in a formula log n=a-bM showing the magnitude frequency relation for earthquakes , 1965 .

[13]  B. Gutenberg,et al.  Frequency of Earthquakes in California , 1944, Nature.

[14]  Rory A. Fisher,et al.  The concepts of inverse probability and fiducial probability referring to unknown parameters , 1933 .