  We analyze the structure of the \emph{frequency space} $Q(F)$ of a nonabelian
free group $F=F(a_1,...,a_k)$ consisting of all shift-invariant Borel
probability measures on $\partial F$ and construct a natural action of $Out(F)$
on $Q(F)$. In particular we prove that for any outer automorphism $\phi$ of $F$
the \emph{conjugacy distortion spectrum} of $\phi$, consisting of all numbers
$||\phi(w)||/||w||$, where $w$ is a nontrivial conjugacy class, is the
intersection of $\mathbb Q$ and a closed subinterval of $\mathbb R$ with
rational endpoints. We also provide an algorithm for detecting strict
hyperbolicity of an automorphism of $F$.
