Discipline: Applied Mathematics
This study aimed to model earthquake occurrences for the next five (5) years in selected areas in Luzon, Philippines using semi-Markov chain. This research focused on estimating the transition matrix, holding time mass functions and interval transition probability matrix for two defined states: region-to-region and magnitude-to-magnitude. Semi-Markov chain was utilized in modeling the earthquakes with magnitude M≥4.0 from 1930-2015 in selected areas in Luzon. The selected areas (13°-16° North latitude by 120°-122° East longitude) were divided into six (6) regions and was used as a state. In addition, magnitudes were classified and used as states (M1<4.6 ; 4.6≤M2≤5.0 ; M3>5.0). From these, the researcher estimated the transition matrices and holding time mass functions. The necessary probability functions were utilized for the determination of interval transition probability matrix. Different dimensions of earthquake like time, location and magnitude were forecasted for the next five (5) years. Based on the findings of the study, the forecasts implies that earthquakes are most probable to happen in some areas of Mindoro and Batangas (13.00°-13.99° North Latitude to 120.00°-120.99° East Longitude) having a magnitude of M>5.0.