The central limit theorem states that the Gaussian law is a good description of the center of the pdf of a sum of a large number N of random variables with finite variance and that the weight (in probability) of the tail goes to zero for large N We now make more precise what is meant by the “center” of the pdf. This section is slightly more technical that the previous ones, eventhough we emphasize a non-rigorous intuitive presentation. The purpose of this chapter is to show that there is a lot of “action” going on in the tails, beyond the central Gaussian region. This must be kept in mind for practical applications and data analysis.
KeywordsCentral Limit Theorem Seismic Moment Extreme Deviation Velocity Increment Lagrange Parameter
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