PARAMETER ESTIMATION OF LOGNORMAL AND PARETO TYPE I DISTRIBUTIONS USING FREQUENTIST AND BAYESIAN INFERENCES

Abstract

Extreme events are events that rarely occur but they cause substantial losses. Insurance companies need to take extreme events into account in risk management because extreme events can have a negative impact on the company's financial health. As a result, insurance companies need an appropriate loss model that matches the empirical data from these extreme events. A distribution that is heavy-tailed and skewed to the right is a good distribution for modeling the magnitude of losses from extreme events. In this paper, two distributions with heavy tails and skew to the right will be used to model the magnitude of losses from extreme events, namely the lognormal distribution and the Pareto distribution type I. The parameters of these distributions are estimated using two inferences, namely the frequentist and Bayesian inferences. In the frequentist inference, two methods are applied, namely the moment method and maximum likelihood. On Bayesian inference, two prior distributions are used, namely uniform and Jeffrey. Test model suitability is carried out by visually comparing the model distribution function with the empirical distribution function, as well as by comparing the Root Mean Square Error (RMSE) value. The visualization results of the distribution function and RMSE values ​​show that in general, the Bayesian inference is better at estimating parameters than the frequentist inference. In the frequentist inference, the maximum likelihood method can provide better estimated values ​​than the moment method. In the Bayesian inference, the two prior distributions show a relatively similar fit to the data and tend to be better than the frequentist inference.