  We describe and discuss the application of Gumbel statistics, which model
extreme events, to WMAP 5-year measurements of the cosmic microwave background.
We find that temperature extrema of the CMB are well modelled by the Gumbel
formalism and describe tests for Gaussianity that the approach can provide.
Comparison to simulations reveals Gumbel statistics to have only weak
discriminatory power for the conventional statistic: $f_{NL}<1000$, though it
may probe other regimes of non-Gaussianity. Tests based on hemispheric cuts
reveal interesting alignment with other reported CMB anomalies. The approach
has the advantage of model independence and may find further utility with
smaller scale data.
