Interevent Time Distribution of Renewal Point Process, Case Study: Extreme Rainfall in South Sulawesi

Abstract

The study of time distribution of occurrences of extreme rain phenomena plays a very important role in the analysis and weather forecast in an area. The timing of extreme rainfall is difficult to predict because its occurrence is random. This paper aims to determine the inter event time distribution of extreme rain events and minimum waiting time until the occurrence of next extreme event through a point process approach. The phenomenon of extreme rain events over a given period of time is following a renewal process in which the time for events is a random variable τ. The distribution of random variable τ is assumed to be a Pareto, Log Normal, and Gamma. To estimate model parameters, a moment method is used. Consider Rt as the time of the last extreme rain event at one location is the time difference since the last extreme rainfall event. if there are no extreme rain events up to t0, there will be an opportunity for extreme rainfall events at (t0, t0 + δt0). Furthermore from the three models reviewed, the minimum waiting time until the next extreme rainfall will be determined. The result shows that Log Nrmal model is better than Pareto and Gamma model for predicting the next extreme rainfall in South Sulawesi while the Pareto model can not be used.