  In this note, we obtain verifiable sufficient conditions for the extreme
value distribution for a certain class of skew product extensions of
non-uniformly hyperbolic base maps. We show that these conditions, formulated
in terms of the decay of correlations on the product system and the measure of
rapidly returning points on the base, lead to a distribution for the maximum of
$\Phi(p) = -\log(d(p, p_0))$ that is of the first type. In particular, we
establish the Type I distribution for $S^1$ extensions of piecewise $C^2$
uniformly expanding maps of the interval, non-uniformly expanding maps of the
interval modeled by a Young Tower, and a skew product extension of a uniformly
expanding map with a curve of neutral points.
