  The problem of inverse statistics (statistics of distances for which the
signal fluctuations are larger than a certain threshold) in differentiable
signals with power law spectrum, $E(k) \sim k^{-\alpha}$, $3 \le \alpha < 5$,
is discussed. We show that for these signals, with random phases, exit-distance
moments follow a bi-fractal distribution. We also investigate two dimensional
turbulent flows in the direct cascade regime, which display a more complex
behavior. We give numerical evidences that the inverse statistics of 2d
turbulent flows is described by a multi-fractal probability distribution, i.e.
the statistics of laminar events is not simply captured by the exponent
$\alpha$ characterizing the spectrum.
