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We study the asymptotic distribution for the occurrence time of the nextlarge earthquake, by knowing the last large seismic event occurred a long timeago. We prove that, under reasonable conditions, such a distribution isasymptotically exponential with a rate depending on the asymptotic slope of thecumulative intensity function corresponding to a non-homogeneous Poissonprocess. Moreover, as it is not possible to obtain an empirical cumulativedistribution function for the waiting time of the next large earthquake, arandom cumulative function based on existing data is stated. We demonstratethat analogous results to the theorems of Glivenko-Cantelli and Kolmogorov aresatisfied by this random cumulative function. We conduct a simulation study fordetecting in what scenario the approximate distribution of the studied elapsedtime performs well. Finally, a real-world data analysis is carried out toillustrate the potential applications of our proposal.

A model for risk assessment of a large earthquake with application to Chilean data