Loss modeling with many-parameter distributions

Abstract

It is argued that many-parameter families of loss distributions may work even with limited amounts of historical data. A restriction to unimodality works as a stabilizer, which makes fitted distributions much more stable than their parameters. We propose Box-Cox transformed Gamma and Burr variables. Those are models with three or four parameters with many of the traditional two-parameter families as special cases, and there are well-defined distributions at the boundaries of the parameter space, which is important for stability. The approach is evaluated with model error defined though the theory of misspecification in statistics. It is shown that such error is drastically reduced when a third or fourth parameter is added without increasing the random error more than a little. It is pointed out that the approach may be a suitable starting point for completely automatic procedures.