  We present measurements of elliptic and triangular azimuthal anisotropy of
charged particles detected at forward rapidity $1<|\eta|<3$ in Au$+$Au
collisions at $\sqrt{s_{_{NN}}}=200$ GeV, as a function of centrality. The
multiparticle cumulant technique is used to obtain the elliptic flow
coefficients $v_2\{2\}$, $v_2\{4\}$, $v_2\{6\}$, and $v_2\{8\}$, and triangular
flow coefficients $v_3\{2\}$ and $v_3\{4\}$. Using the small-variance limit, we
estimate the mean and variance of the event-by-event $v_2$ distribution from
$v_2\{2\}$ and $v_2\{4\}$. In a complementary analysis, we also use a folding
procedure to study the distributions of $v_2$ and $v_3$ directly, extracting
both the mean and variance. Implications for initial geometrical fluctuations
and their translation into the final state momentum distributions are
discussed.
