PARAMETER ESTIMATION OF TWEEDIE DISTRIBUTION USING PROFILE LIKELIHOOD METHOD ON PEAK GROUND ACCELERATION (PGA) DATA: CASE OF THE 2009 PADANG EARTHQUAKE

• Main Author: ANDRIANI (NIM:10114047), IVENNIA
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/28190
• Institution: Institut Teknologi Bandung

A Tweedie probability model is a special case of the exponential dispersion model which could be used to model the response random variable in a Generalized Linear Model (GLM). However, the probability density function of a Tweedie distribution does not have an explicit analytic form. Hence, the estimation of the parameters p and ? in a Tweedie distribution need to be carried out numerically. Two of such methods are the Profile Likelihood method and the Nelder-Mead Algorithm. For the estimation of the parameter µ in the Tweedie probability model, the Maximum Likelihood Estimation (MLE) method can be used analytically. In this final project, a Lognormal distribution and a Tweedie probability model are fitted to the Peak Ground Acceleration (PGA) data of the 2009 Padang earthquake. PGA as one of the ground movement parameters is the largest absolute value of acceleration recorded on the accelerogram. It is obtained that for the Lognormal distribution, the estimates of its parameters are ? ?= 2.140571 and (?^2 ) ? = 0.428797. As for the Tweedie distribution, it is obtained that ? ? = 10.572157, while the estimates of the parameters p and ? using the Profile Likelihood are p ? = 3.644898 and ? ? = 0.013471, respectively. Using the Nelder-Mead Algorithm, the corresponding estimates are p ? = 3.618445 and ? ? = 0.014191. Throughout the data processing using RStudio, it was observed that the process time needed for Profile Likelihood method is longer than that for the Nelder-Mead Algorithm; but the Nelder-Mead Algorithm needs an initial value in order to start the iteration. The Anderson-Darling and Cramér-von Mises tests showed that for significance levels of ? = 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.