Treatment of the Data Collection Threshold in Operational Risk : A Case Study with the Lognormal Distribution

Among operational risk practitioners there is some confusion about the implications of the loss data collection threshold and the estimation of "truncated" or "shifted" distributions. Claims that "shifted" models result in biased parameter estimates rely on the premise that the "true" model is known to be "truncated" and do not objectively evaluate "shifted" distributions. We systematically analyze the performance of "shifted" and "truncated" lognormal models and illustrate the use of Vuong's LR test for model selection. We conclude that truncated and shifted lognormal models are equally valid or invalid approaches for estimating loss severity with a data collection threshold