| A Preliminary Discussion of Heavy- and Light-Tailed Distributions |
| Written by theoretic |
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The Danish fire insurance data and the US industrial fire data presented in Figures 3.2.5 and 3.2.15, respectively, can be modeled by a very heavy-tailed distribution. Such claim size distributions typically occur in a reinsurance portfolio, where the largest claims are insured. In this context, the question arises: What determines a heavy-tailed/light-tailed claim size distribution? There is no clear-cut answer to this question. One common way to characterize the heaviness of the tails is by means of the exponential distribution as a benchmark. For example, if F(x) limsup г— < oo for some A > 0, — ЛХ x—>oo e where F(x) = 1 — F(x), x > 0, denotes the right tail of the distribution function F, we could call F light-tailed, and if F(x) liminf г— > 0 for all A > 0, x^cx, e ~Xx we could call F heavy-tailed. Example 3.2.4 (Some well-known heavy- and light-tailed claim size distributions) From the above definitions, the exponential Exp(A) distribution is light-tailed for every A > 0. |