  We study non-local properties of generic three-qubit pure states. First, we
obtain the distributions of both the coefficients and the only phase in the
five-term decomposition of Ac\'in et al. for an ensemble of random pure states
generated by the Haar measure on U(8). Furthermore, we analyze the probability
distributions of two sets of polynomial invariants. One of these sets allows us
to classify three-qubit pure states into four classes. Entanglement in each
class is characterized using the minimal R\'enyi-Ingarden-Urbanik entropy.
Besides, the fidelity of a three-qubit random state with the closest state in
each entanglement class is investigated. We also present a characterization of
these classes and the SLOCC classes in terms of the corresponding entanglement
polytope.
