  By means of the multifractal analysis (MFA), the expressions of the
probability density functions (PDFs) are unified in a compact analytical
formula which is valid for various quantities in turbulence. It is shown that
the formula can explain precisely the experimentally observed PDFs both on log
and linear scales. The PDF consists of two parts, i.e., the {\it tail} part and
the {\it center} part. The structure of the tail part of the PDFs, determined
mostly by the intermittency exponent, represents the intermittent large
deviations that is a manifestation of the multifractal distribution of
singularities in physical space due to the scale invariance of the
Navier-Stokes equation for large Reynolds number. On the other hand, the
structure of the center part represents small deviations violating the scale
invariance due to thermal fluctuations and/or observation error.
