In order to reveal the underlying statistics properly describing fully deve
loped turbulence, the probability density function of the local dissipation
is determined by taking the extreme of a generalized entropy (Tsallis entr
opy). With the density function, the scaling exponents zeta (m) of the velo
city structure function are derived analytically. It is found that these sc
aling exponents are consistent with experimental data. The asymptotic expre
ssion of zeta (m) for m >> 1 has a log term.