Fitting Distribusi pada Waktu Antar Kedatangan Peristiwa Gempa Menggunakan Metode Maksimum Likelihood

Abstract

This study aims to fit the distribution on the inter-arrival time of earthquake events in North Sumatra using the maximum likelihood method. Parameter estimation is a method to determine population values using sample values. The gamma distribution and exponential distribution can be estimated by the maximum likelihood method because they have a continuous probability density function. Most parts of Indonesia have a relatively high level of seismicity, one of which is in North Sumatra. Seismic activity is based on analysis of the time between arrivals which describes a pattern. In this study, the data used is earthquake data in the period  1 January 2019 – 31 December 2022 by calculating the time between arrivals of earthquake events. Based on the estimation results on the gamma distribution, the value of α ̂= 438,7274 and the value of β ̂= 0.3599 and on the exponential distribution and the value of θ ̂ = 157,898. Then based on the AIC method, the selected distribution is an exponential distribution with an AIC value=0.79 with estimated parameters on the exponential distribution showing that the estimated parameters on the exponential distribution showing that the estimated occurrence of earthquakes with an average time of occurance of 157.8274 hours.