  Operational risk models commonly employ maximum likelihood estimation (MLE)
to fit loss data to heavy-tailed distributions. Yet several desirable
properties of MLE (e.g. asymptotic normality) are generally valid only for
large sample-sizes, a situation rarely encountered in operational risk. In this
paper, we study how asymptotic normality does--or does not--hold for common
severity distributions in operational risk models. We then apply these results
to evaluate errors caused by failure of asymptotic normality in constructing
confidence intervals around the MLE fitted parameters.
