Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world

Estimation in the three-parameter inverse Gaussian distribution

A mixed moments method for the estimation of parameters in the three-parameter inverse Gaussian distribution (IG3) is introduced. The method is an adaptive iterative procedure, which combines the method of moments with a regression method based on the empirical moment generating function. Monte Carlo results indicate that the new procedure is more efficient than alternative estimation methods (including the maximum likelihood) over large portions of the parameter space with samples of small or moderate size. Asymptotic results are also obtained and may be used to draw approximate inferences with small samples. Two data sets are used to illustrate estimation and testing procedures and to construct exploratory graphs for the appropriateness of the IG3 model. © 2004 Elsevier B.V. All rights reserved