Treatment of the data collection threshold in operational risk: a case study using the lognormal distribution

Alexander Cavallo, Benjamin Rosenthal, Xiao Wang and Jun Yan

Abstract

ABSTRACT

There is some confusion among operational risk practitioners regarding 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 likelihood ratio 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.