Keywords: finite mixture models, EM algorithm, loss modeling, grouped data
Previous research on mixture modeling with grouped data considered the information about the frequency of the observations for each interval in which they fall. These models have limitations when the additional information is available about the grouped data, such as average value of the observations for each interval in which they fall. We propose an extension of the existing mixture models for grouped data that will incorporate the information about the average value of all observations for each corresponding interval. A transformation method is proposed for transforming the grouped data into individual data, under the constraint that the given average value of the observations within each interval is maintained. The finite mixture model with the EM algorithm has been applied to the transformed data using Gamma, Lognormal, and Weibull distributions. The results of the simulation study confirmed a good performance of the proposed methods. A real data set on insurance loss amounts, reported for bodily injury liability, is modeled using our proposed approach.