Statistical properties of the Lyapunov exponent lambda in Hamiltonian systems are studied numerically. Anomalous distributions of lambda are discussed from multi-ergodic aspects of Hamiltonian chaos. The fluctuation of lambda reveals a 1/f spectrum and the anomalous convergence. The results imply that the most probable value of the Lyapunov exponent approaches zero when the averaging time goes to infinity. Orbital weak instability for the multi-ergodic motion is discussed in relation to the A-entropy.