COMPARISON OF MAXIMUM LIKELIHOOD ESTIMATION AND METHOD OF MOMENTS FOR ESTIMATING PARETO DISTRIBUTION PARAMETERS ON MEDICAL MALPRACTICE CLAIMS

Abstract

Medical Malpractice Claims present unique challenges for healthcare providers and insurance carriers because of their uncertain nature. Large financial losses arising from a high claim count are difficult to quantify. Therefore, an appropriate distribution model and estimation method are essential for effective risk management and planning. One of the significant distribution models is Pareto Distribution, having estimation techniques such as Maximum Likelihood Estimation (MLE) and Method of Moments (MoM). The objective of this study is to investigate the potential performance disparity between two major types of methods that is Maximum Likelihood Estimation and Method of Moments for estimating Pareto distribution parameters on medical malpractice claims data as applied specifically to the frequency-of-claims problem, focusing particularly on claim ages falling within age interval 36–65 years. The evaluation is done based on error metrics that is Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). The analysis results show that MAE value for MoM is 0.02065, while for MLE is 0.01883. The MAPE calculation results show that the prediction value of MoM is 63%, while that of the MLE is 57%. In addition, the MSE value for MoM is 0.00060 and for the MLE is 0.00047. Last, the RMSE value for MoM is 0.02440, while for the MLE is 0.02163. Furthermore, the MAPE exceeding 50% indicates both methods are less effective for this particular case. However, based on the MAE, MSE, and RMSE results in this study, MLE and MoM show almost the same accuracy, so both methods can be considered equally good for parameter estimation. Nonetheless, in general, MLE is often considered a better method than MoM due to its more comprehensive approach in theory.