Composite Tukey-type distributions with application to operational risk management

Similarly to many other quantitative disciplines, operational risk modeling requires flexible distributions defined for non-negative values, which enable heavy-tail behavior. Because they can account for the different requirements related to “extreme†observations in the tail and “ordinary†observations in the body of such distributions, so-called composite or spliced models have gained increasing attention in recent years. The focus of this paper is on composite Tukey-type distributions. This term describes a class of distributions whose tails follow a generalized truncated Tuke-ytype distribution, which allows for greater flexibility than the commonly used generalized Pareto distribution. After reviewing the classical Tukey-type family, we discuss the leptokurtic properties that emerge from a general kurtosis transformation, and we study several estimation methods for the truncated Tukey-type distribution. Finally, we empirically demonstrate the flexibility of our new composite model with an operational risk data set and business interruption losses.