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The heavy-tail nature of the data causes the following statistical problems.

• Instability of estimates: The differences between the mean and variance of the distribution can be dramatically different from including just a single, large extreme loss. Hence, the sample statistics (e.g., mean, variance, etc.) will be quite volatile.

• Dominance of sums: Within the same process, the largest few (e.g., ten losses) may account for 50% or more of the total losses in a given business line. Hence, the total loss is largely driven by relatively few observations in the data set.

• Dominance of mixtures: Consider two processes: one that is heavy-tailed, and one that is light-tailed. If the two processes are aggregated, then it is clear that the heavy-tailed distribution will overwhelm the stable properties of the light-tailed distribution. In fact, it is not uncommon for the single, largest loss to account for the majority of total losses across the entire financial institution.