Comparison of Tail Performance of the Champernowne Transformed Kernel Density Estimator, the Generalized Pareto Distribution and the G-and-H Distribution

Several papers have recommended the Champernowne distribution to describe operational risklosses. This paper compares the tail performance of the Champernowne transformed kernel density estimator, the generalized Pareto distribution (gpd) and the g-and-h distribution. We introduce a new tail dependent parameter estimation method for the Champernowne distribution, computed by conditional maximum likelihood, and show that, by using this new method, we obtain an estimator that in general outperforms the benchmark estimators with respect to tail performance. At the same time the new estimator provides a density estimate on the entire axis superior to the g-and-h distribution, and unlike the gpd estimator, which provides a density estimate only above the threshold. The estimators performance are investigated in a Monte Carlo simulation study, and their application to operational risk is illustrated