Analysis of Gutenberg-Richter b-value and mmax

Part III: Non-positive Gutenberg-Richter b-value

Abstract

When we analyzed the Gutenberg-Richter distribution function in our earlier works, we assumed that the b-value is positive.  Using generalized estimators, we found that in some cases the b-value can be also negative. This paper gives a theoretical background for the negative b-value. We show also expand (the expansion of) the KS functions on the interval . Moreover, we show how to design the code to use these new series, especially how to manage the case of .