An exploration of non-exponential family distributions in run-off triangle.

Abstract

The conventional way to model claims liabilities is by using distributions from the exponential family to fit run-off triangles. In this research, we explore the possibilities of using distributions from non-exponential family to model claim liabilities. Five such distributions are applied to three sets of claims run-off data and the R statistical programming software is used to generate the data analysis. Using Maximum Likelihood Estimation (MLE), we derive the estimated parameters of claims distributions and calculated outstanding claim liabilities of each distribution. Next, using the comparison methods - Mean Absolute Percentage Error (MAPE), Standardized Residual Analysis and t-Statistics Test, we seek the best non-exponential family distribution. We were thus able to identify that Laplace distribution is the best fit to model claim liabilities. In addition, our findings have highlighted some precautions that users should note when using a non-exponential distribution to fit claim liabilities.