Analysis of Gutenberg-Richter b-value and mmax Part IV: New technique to estimate the parameters mmax, mmin and b-value

Abstract

In this paper, we carried out an analysis of the Gutenberg-Richer distribution function, which gives a new technique to estimate the expected values. This estimator, which we referred to as expected value curve estimator, gives a relationship between the Order Statistic and the Maximum Statistic. Also, it was observed that the sample size is unknown parameter in the real seismic catalogs. In addition,  we show an algebraic solution for the Gutenberg-Richter distribution problem, where all the unknown parameters ,  and  are estimated using four estimators of the expected values. We also discuss the role of the negative b-value.