  An analytical formula for the probability density function (PDF) of the
velocity fluctuation in fully-developed turbulence is derived,
non-perturbatively, by assuming that its underlying statistics is the one based
on the generalized measures of entropy, the R\'{e}nyi entropy or the
Tsallis-Havrda-Charvat (THC) entropy. The parameters appeared in the PDF,
including the index $q$ which appears in the measures of the R\'{e}nyi entropy
or of the THC entropy are determined self-consistently with the help of the
observed value $\mu$ of the intermittency exponent. The derived PDF explains
quite well the experimentally observed density functions.
