Estimation of Generalized Pareto Distribution Parameters in Traffic Accident Loss Data Modeling

Abstract

The problem of traffic accidents in Indonesia has a high level of risk. In an effort to minimize losses due to traffic accidents, it is necessary to study the data and characteristics of traffic accidents and identify these events as extreme events. This study was conducted to find out how to estimate the shape and scale parameters using Maximum Likelihood Estimation (MLE), and to explore data on traffic accident losses in Indonesia. The method used to analyze the extreme value of traffic accident losses is the Extreme Value Theory. One approach to identify extreme values is Peaks Over Threshold which follows the Generalized Pareto Distribution (GPD). Traffic accident loss data is divided into three types based on the cause, namely driver negligence, vehicle quality, and other external factors in the period (2008-2017). Estimation of shape and scale parameters is obtained through MLE which is then solved by Newton Raphson because it produces equations that are not closed form. This study resulted in an estimate of the shape and scale of the GPD distribution parameter, as well as a confidence interval (1-α) of 100% with of 5%. In addition, it is concluded that the parameters obtained from the estimation have the same characteristics for each type of risk analyzed, but have different parameter values. Based on parameter estimation, GPD distribution is obtained from each risk which is expected to be useful for related parties in analyzing the number of traffic accident losses in the next period to consider steps that can be taken to reduce losses due to traffic accidents.