2016/02/09 by Raúl Fierro, Fierro, Raúl, Víctor Leiva +1
Computer Science · Earth and Planetary Sciences · #FOS: Mathematics #Geochemistry and Geologic Mapping #Geological and Geophysical Studies Worldwide #Statistics Theory (math.ST) #earthquake and tectonic studies
paper · pdf · doi:10.48550/arxiv.1602.02861
openalex publication_date 2016/02/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study the asymptotic distribution for the occurrence time of the next large earthquake, by knowing the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is asymptotically exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a non-homogeneous Poisson process. Moreover, as it is not possible to obtain an empirical cumulative distribution function for the waiting time of the next large earthquake, a random cumulative function based on existing data is stated. We demonstrate that analogous results to the theorems of Glivenko-Cantelli and Kolmogorov are satisfied by this random cumulative function. We conduct a simulation study for detecting in what scenario the approximate distribution of the studied elapsed time performs well. Finally, a real-world data analysis is carried out to illustrate the potential applications of our proposal.