We show that both the slip distribution and the peak ground acceleration (PGA) for the 1999 Chi Chi earthquake can be described by L¿vy laws. Furthermore, we found that the tails of the probability density functions (PDF) characterizing the slip and the ∣PGA∣ are governed by a parameter, the L¿vy index, with almost the same values as predicted by the Central Limit theorem. The PDF tail controls the frequency at which extreme large events can occur. These events are the large stress drops--asperities--distributed over the fault surface and the large ∣PGA∣ observed in the ground motion. Our results suggest that the frequency of these events is coupled; the PDF of the ∣PGA∣ is a direct consequence of the PDF of the asperities. The physical rationale responsible for the coupling is the principle of superposition of wave signals characterized by random properties that are governed by the Central Limit theorem.