  Asteroid families form as a result of large-scale collisions among main belt
asteroids. The orbital distribution of fragments after a family-forming impact
could inform us about their ejection velocities. Unfortunately, however, orbits
dynamically evolve by a number of effects, including the Yarkovsky drift,
chaotic diffusion, and gravitational encounters with massive asteroids, such
that it is difficult to infer the ejection velocities eons after each family's
formation. Here we analyze the inclination distribution of asteroid families,
because proper inclination can remain constant over long time intervals, and
could help us to understand the distribution of the component of the ejection
velocity that is perpendicular to the orbital plane ($v_{W}$). From modeling
the initial breakup, we find that the distribution of $v_{W}$ of the fragments,
which manage to escape the parent body's gravity, should be more peaked than a
Gaussian distribution (i.e., be leptokurtic) even if the initial distribution
was Gaussian. We surveyed known asteroid families for signs of a peaked
distribution of $v_{W}$ using a statistical measure of the distribution
peakedness or flatness known as kurtosis. We identified eight families whose
$v_{W}$ distribution is significantly leptokurtic. These cases (e.g. the
Koronis family) are located in dynamically quiet regions of the main belt,
where, presumably, the initial distribution of $v_{W}$ was not modified by
subsequent orbital evolution. We suggest that, in these cases, the inclination
distribution can be used to obtain interesting information about the original
ejection velocity field.
