A pentatonic classification of extreme events

In this paper we present a classification of the extreme events – very small and very large outcomes – of positive-valued random variables. The classification distinguishes five different categories of randomness, ranging from the very ‘mild’ to the very ‘wild’. In analogy with the common five-tone musical scale we term the classification ‘pentatonic’. The classification is based on the analysis of the inherent Gibbsian ‘forces’ and ‘temperatures’ existing on the logarithmic scale of the random variables under consideration, and provides a statistical-physics insight regarding the nature of these random variables. The practical application of the pentatonic classification is remarkably straightforward, it can be performed by non-experts, and it is demonstrated via an array of examples.