IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Introduction to extreme value theory
For block maxima of independent, identically distributed losses, the Fisher-Tippett-Gnedenko theorem states that, after suitable normalisation, the limiting distribution of the maximum (if it exists and is non-degenerate) belongs to which family?
The limiting distribution of normalised block maxima of iid losses is the Generalised Extreme Value family, covering the Gumbel, Fréchet and Weibull types. The Generalised Pareto distribution applies to exceedances over a high threshold, not to block maxima.
- AThe normal family
- BThe Generalised Extreme Value (GEV) familyCorrect
- CThe Generalised Pareto family
- DThe Poisson family
- The chi-squared family
Explanation
The Fisher-Tippett-Gnedenko theorem shows that normalised block maxima converge to a GEV distribution, which combines the Gumbel, Fréchet and Weibull types. The Generalised Pareto family describes threshold exceedances, not block maxima, so it is the tempting but wrong choice.
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