Journal of Operational Risk

Composite Tukey-type distributions with application to operational risk management

Linda Möstel, Matthias Fischer and Marius Pfeuffer

  • The focus of this paper is on spliced distributions where the tail distribution is modelled by a (truncated) Tukey-type distribution.
  • Different methods to estimate the unknown parameters are introduced and evaluated.
  • Application to operational and insurance loss data sets illustrates the flexibility of the Tukey-type tails against Generalized Parato tails.

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.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here