PARAMETER ESTIMATION OF TWEEDIE DISTRIBUTION USING NELDER-MEAD ALGORITHM ON PEAK GROUND ACCELERATION (PGA) DATA: CASE OF THE 2009 PADANG EARTHQUAKE - ERLANGGA WIJAYA HERRYAGUNG, MARCELLINO
An earthquake is a catastrophic natural disaster which may cause financial losses, environmental damages, and even deaths. The Peak Ground Acceleration (PGA) is one of the parameters of a ground motion magnitude. The PGA in a particular location is determined by the moment magnitude of the earthquake, the distance of the location from the epicenter, and the type of soil at the location. In this Final Project, the PGA data of the 2009 Padang earthquake is modeled using a Lognormal L(?,?^2) and a Tweedie ED_p (?,?) distribution. The estimate of the parameters ? and ?^2 in the Lognormal distribution and the parameter ? in the Tweedie distribution are obtained using the Maximum Likelihood Estimation (MLE) method analytically. The parameters p and ? in the Tweedie distribution are estimated using the Nelder-Mead Algorithm and then compared with those obtained by the Profile Likelihood method. It is obtained that for the Lognormal distribution, ? ?=2.140571 and (?^2 ) ?=0.428797; and for the Tweedie distribution, ? ?=10.572157. Using the Nelder-Mead Algorithm, the estimates of the parameters p and ? are p ?=3.618445 and ? ?=0.014191, respectively; whereas using the Profile Likelihood method, are p ?=3.644898 and ? ?=0.013471, respectively. The Anderson-Darling and CramÃƒÂ©r-von Mises tests showed that, for the levels of significance ?=0.01, 0.05, and 0.1, the PGA data of the 2009 Padang earthquake could not be modeled by a Lognormal nor a Tweedie distribution.