**Abstract**

This chapter aims to provide a methodology to test the probability distributions of earthquakes in terms of the interoccurrence times (ITs), namely, the time between consecutive earthquakes of a specific magnitude. First, we compile a new earthquake catalog for the El Salvador subduction zone within moment magnitude M 5.0–8.12 comprising historical and instrumental data for 1609–2019. Secondly, we explain the fundamentals of the Weibull and Poisson distributions and verify the IT probability fits when considering the clustered catalog. We find that the Weibull distribution fits all ITs, while the Poisson distribution fails to explain the natural seismicity patterns for small magnitude bins. Besides, we test the assumption that the declustering process leads to a Poisson probability distribution when removing foreshocks and aftershocks in the earthquake catalog. Finally, the classical Gutenberg–Richter relationship and conditional magnitude probabilities are calculated as an essential input in any seismic hazard assessment.

**Keywords:** earthquake catalog, Weibull and Poisson probability distribution, subduction zone, interoccurrence times
