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We establish some statistical properties of the hyperbolic times for a classof nonuniformly expanding dynamical systems. The maps arise as factors of areapreserving maps of the unit square via a geometric Baker's map typeconstruction, exhibit intermittent dynamics, and have unbounded derivatives.The geometric approach captures various examples from the literature over thelast thirty years. The statistics of these maps are controlled by the order oftangency that a certain "cut function" makes with the boundary of the square.Using a large deviations result of Melbourne and Nicol we obtain sharpestimates on the distribution of first hyperbolic times. As shown by Alves,Viana and others, knowledge of the tail of the distribution of first hyperbolictimes leads to estimates on the rate of decay of correlations and derivation ofa CLT. For our family of maps, we compare the estimates on correlation decayrate and CLT derived via hyperbolic times with those derived by a direct Youngtower construction. The latter estimates are known to be sharp.

First hyperbolic times for intermittent maps with unbounded derivative