  Typically, operational risk losses are reported above a threshold. Fitting
data reported above a constant threshold is a well known and studied problem.
However, in practice, the losses are scaled for business and other factors
before the fitting and thus the threshold is varying across the scaled data
sample. A reporting level may also change when a bank changes its reporting
policy. We present both the maximum likelihood and Bayesian Markov chain Monte
Carlo approaches to fitting the frequency and severity loss distributions using
data in the case of a time varying threshold. Estimation of the annual loss
distribution accounting for parameter uncertainty is also presented.
