The truncated g-and-h distribution: estimation and application to loss modeling

The g-and-h distribution is a flexible model for skewed and/or leptokurtic data, which has been shown to be especially effective in actuarial analytics and risk management. Since in these fields data are often recorded only above a certain threshold, we introduce a left-truncated g-and-h distribution. Given the lack of an explicit density, we estimate the parameters via an Approximate Maximum Likelihood approach that uses the empirical characteristic function as summary statistics. Simulation results and an application to fire insurance losses suggest that the method works well and that the explicit consideration of truncation is strongly preferable with respect the use of the non-truncated g-and-h distribution.